physics

1. Ib lub pob ncaws pob uas raug ncaws tawm hauv av ntawm lub kaum sab xis θ = 30^o mus rau kab rov tav nrog qhov ceev pib ntawm 14 m/s. Xam qhov ceev kawg ua ntej lub pob ntaus hauv av.

Paub:

Lub kaum sab xis (θ= 3 TZS0^o

Qhov ceev pib (v_o) = 14 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Xav tau: Qhov ceev kawg ua ntej lub pob ntaus hauv av

Tshuaj:

Kab rov tav ntawm qhov ceev pib:

v_ox = v_o cos θ = (14 m/s)(cos 30^o) = (14 m/s)(0.5√3= 7 TZS√3 m / s

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (14 m/s)(sin 30^o) = (14 m/s)(0.5) = 7 m/s

Qhov ceev kawg ntawm kev taw qhia ntsug

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 7 m/s (zoo rau sab saud)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Qhov siab (h) = 0 (khoom rov qab mus rau qhov chaw pib)

Xav tau: Qhov ceev kawg (v_t)

Tshuaj:

v_t² = v_o² + 2 gh = 7² + 2(-10)(0) = 49 – 0 = 49

v_t = √49 = 7 m/s

Qhov ceev kawg ntawm kab rov tav

Qhov ceev pib ntawm kab rov tav yog 7√3 m/s. Qhov ceev yog qhov ruaj khov yog li qhov ceev kawg yog tib yam li qhov ceev pib.

Qhov ceev kawg ua ntej lub khoom ntaus hauv av

2. Ib lub cev raug tsa rau saum ntuj ntawm lub kaum sab xis ntawm 30^o nrog rau kab rov tav los ntawm lub tsev siab 5 meters. Nws qhov ceev pib yog 10 m/s. Xam qhov ceev kawg ua ntej lub khoom ntaus hauv av! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ= 30 TZS^o

Qhov siab pib (h_o) = 5 meters

Qhov ceev pib (v_o) = 10 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Qhov ceev kawg

Tshuaj:

Kab rov tav ntawm qhov ceev pib:

v_ox = v_o cos θ = (10 m/s)(cos 30^o) = (10 m/s)(0.5√3= 5 TZS√3 m / s

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (10 m/s)(sin 30^o) = (10 m/s)(0.5) = 5 m/s

Qhov ceev kawg ntawm kev taw qhia ntsug

Paub:

Qhov ceev pib (v_o) = 5 m/s (zoo rau sab saud)

acceleration ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Qhov siab (h) = -5 m (tsis zoo vim tias hauv av qis dua qhov siab pib)

Xav tau: Qhov ceev kawg (v_t)

Tshuaj:

v_t² = v_o² + 2 gh = 5² + 2(-10)(-5) = 25 + 100 = 125

v_t = √125 m/s

Qhov ceev kawg ntawm kab rov tav

Qhov ceev kawg ntawm kab rov tav yog 53 m/s.

Qhov ceev kawg

3. Ib lub pob me me uas raug tso tawm kab rov tav nrog qhov ceev pib v_o = 8 m/s ntawm lub tsev siab 12 meters. Xam qhov ceev kawg ua ntej lub pob ntaus hauv av! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m / s²

Paub:

Qhov siab (h) = 12 meters

Qhov ceev pib (v_o) = 8 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Qhov ceev kawg (v_t)

Tshuaj:

Kab rov tav ntawm qhov ceev pib:

v_ox = v_o = 8 m/s

Feem ntsug ntawm qhov ceev pib:

v_oy = 0 m/s

Qhov ceev kawg ntawm kev taw qhia ntsug

xam siv qhov sib npaug ntawm kev txav mus los dawb.

Paub:

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Qhov siab (h) = 12 m

Xav tau: Qhov ceev kawg (v_t)

Tshuaj:

v_t² = 2 gh = 2(10)(12) = 240

v_t = √240 m/s

Qhov ceev kawg ntawm kab rov tav

Qhov ceev pib hauv kab rov tav yog 8 m/s. Qhov ceev yog tas li kom qhov ceev pib sib npaug rau qhov ceev kawg. Yog li qhov ceev kawg ntawm kab rov tav yog 8 m/s.

Qhov ceev kawg

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv

Tau daws cov teeb meem hauv kev txav mus los ntawm projectile - txiav txim siab qhov chaw ntawm ib yam khoom

1. Ib lub cev raug nthuav mus rau saum ntuj ntawm lub kaum sab xis ntawm 60^o rau kab rov tav nrog qhov ceev pib ntawm 12 m/s. Txheeb xyuas qhov chaw ntawm yam khoom tom qab txav mus rau 1 vib nas this! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 60^o

Initial tshaj tawm (v_o) = 12 m/s

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Xav tau: Qhov chaw ntawm yam khoom tom qab txav mus rau 1 vib nas this

Tshuaj:

Kab rov tav ntawm qhov ceev pib:

v_ox = v_o cos θ = (12 m/s)(cos 60^o) = (12 m/s)(0.5) = 6 m/s

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (12 m/s)(sin 60^o) = (12 m/s)(0.5√3= 6 TZS√3 m / s

Qhov chaw ntawm cov khoom ntawm kab rov tav:

Paub:

Kab rov tav ntawm qhov ceev (v)_x) = 6 m/s

Lub sijhawm luv (t) = 1 vib nas this

Xav tau: kab rov tav (x)

Tshuaj:

6 meters/ob txhais tau tias lub pob txav mus deb li 6 meters txhua 1 vib nas this. Qhov deb ntawm lub pob tom qab txav mus rau 1 vib nas this yog 6 meters. Yog li qhov chaw ntawm lub pob nyob rau hauv kev taw qhia kab rov tav yog 6 meters.

Qhov chaw ntawm cov khoom ntawm qhov kev taw qhia ntsug:

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 6√3 m/s (zoo rau sab saud)

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m/s² (tsis zoo downward)

Xav tau: qhov siab tom qab txav mus rau 1 vib nas this

Tshuaj:

h = v_o t + 1/2 gt² = (6√3)(1) + 1/2 (-10)(1²) = 6√3 + (-5)(1) = 6√3 – 5 = 6(1.7) – 5 = 10.2 – 5 = 5.2 meters.

Qhov chaw ntawm yam khoom tom qab txav mus rau 1 vib nas this:

Kev hloov kab rov tav (x) = 6 meters

Kev hloov chaw ntsug (y) = 5.2 meters

2. Ib lub cev raug nthuav mus rau saum ntuj ntawm lub kaum sab xis ntawm 30^o rau kab rov tav ntawm lub tsev siab 20 meters. Nws qhov ceev pib yog 50 m/s. Xam qhov kev hloov pauv ntsug tom qab lub cev txav mus rau 1 vib nas this! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 30^o

Qhov siab pib (h_o) = 20 meters

Qhov ceev pib (v_o) = 50 m / s

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Xav tau: Qhov siab (h)

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (50 m/s)(sin 30^o) = (50 m/s)(0.5) = 25 m / s

Qhov siab:

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 25 m/s (zoo rau sab saud)

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Xav tau: Qhov siab (h)

Tshuaj:

h = v_o t + 1/2 gt² = (25)(1) + 1/2 (-10)(1)²) = 25 + (-5)(1) = 25 – 5 = 20 meters.

Qhov siab ntawm lub cev tom qab txav mus rau 1 vib nas this yog 20 meters saum toj no qhov twg lub cev nyob kwv yees los yog 40 meters saum av.

3. Ib lub pob me me uas raug tso tawm kab rov tav nrog qhov ceev pib v_o = 10 m/s ntawm lub tsev siab 10 meters. Xam qhov kev hloov pauv ntawm lub pob tom qab txav mus 1 vib nas this! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m / s²

Paub:

Qhov siab pib (h) = 10 meters

Qhov ceev pib (v_o) = 10 m/s

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

SE pob: Qhov chaw ntawm lub pob tom qab txav mus 1 vib nas this!

Tshuaj:

Kev hloov chaw kab rov tav:

Paub:

Kab rov tav ntawm qhov ceev (v)_x) = 10 m/s

Lub sijhawm luv (t) = 1 vib nas this

SE pob: Qhov chaw ntawm yam khoom

Tshuaj:

10 meters/ib vib nas this txhais tau tias yam khoom txav mus deb txog li 10 meters txhua 1 vib nas this. xaav tom qab txav mus rau 1 vib nas this yog 10 meters. Yog li ntawd, qhov kev hloov pauv kab rov tav yog 10 meters.

Kev hloov pauv ntsug:

Xam raws li qhov kev txav mus los dawb.

Paub:

Lub sijhawm luv (t) = 1 vib nas this

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Qhov siab tom qab txav mus rau 1 vib nas this (h)

Tshuaj:

h = 1/2 gt² = 1/2 (10)(1)²) = (5)(1) = 5 meters.

Tom qab 1 vib nas this, yam khoom ntawd poob mus txog 5 meters. Qhov siab saum av = 10 meters – 5 meters = 5 meters.

Qhov chaw ntawm cov khoom tom qab txav mus los 1 vib nas this:

Qhov chaw ntawm yam khoom ntawm kev taw qhia kab rov tav (x) = 10 meters

Qhov chaw ntawm cov khoom ntawm qhov kev taw qhia ntsug (y) = 5 meters

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv

Tau daws cov teeb meem hauv kev txav mus los ntawm projectile - txiav txim siab lub sijhawm sib nrug

1. Ib lub pob ncaws pob uas raug ncaws tawm hauv av ntawm lub kaum sab xis θ = 30^o mus rau kab rov tav nrog qhov ceev pib ntawm 10 m/s. Xam lub sijhawm kom mus txog qhov siab tshaj plaws! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 30^o

Qhov ceev pib (v_o) = 10 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Lub sijhawm mus txog qhov chaw qhov siab tshaj plaws

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (10 m/s)(sin 30^o) = (10 m/s)(0.5) = 5 m / s

Lub sijhawm kom mus txog qhov siab tshaj plaws yog txiav txim siab los ntawm kev txav mus los ntsug cov qauv sib npaug. Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau hauv qab ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 5 m / s (zoo sab saud)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Qhov ceev kawg ntawm qhov siab tshaj plaws (v_t= 0 TZS

Xav tau: lub sijhawm luv (t)

Tshuaj:

v_t = v_o + gt

0 = 5 + (-10)t

0 = 5 – 10 t

5 = 10 t

t = 5/10 = 0.5 vib nas this

2. Ib lub cev raug nthuav mus rau saum ntuj ntawm lub kaum sab xis ntawm 30^o rau kab rov tav nrog qhov ceev pib ntawm 30 m/s. Xam lub sijhawm ya! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 30^o

Qhov ceev pib (v_o) = 8 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Xav tau: Lub sijhawm ua ntej lub cev poob rau hauv av

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (8 m/s)(sin 30^o) = (8 m/s)(0.5) = 4 m / s

Peb xub xam lub sijhawm kom mus txog qhov siab tshaj plaws siv cov qauv ntawm kev txav ntsug.

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 4 m / s (zoo sab saud)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Qhov ceev kawg ntawm qhov siab tshaj plaws (v_t= 0 TZS

Xav tau: Lub sijhawm luv (t)

Tshuaj:

v_t = v_o + gt

0 = 4 + (-10)t

0 = 4 – 10 t

4 = 10 t

t = 4/10 = 0,4 vib nas this

Lub sijhawm luv mus txog qhov siab tshaj plaws yog 0.4 vib nas this.

Lub sijhawm nyob hauv huab cua yog 2 x 0.4 s = 0.8 s.

3. Ib lub cev raug nthuav mus rau saum ntuj ntawm lub kaum sab xis ntawm 30^o nrog rau kab rov tav los ntawm lub tsev siab 10 meters. Nws qhov ceev pib yog 40 m/s. Nws siv sijhawm ntev npaum li cas lub cev thiaj li mus txog hauv av? Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 30^o

Qhov siab pib (h_o) = 10 meters

Qhov ceev pib (v_o) = 40 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Xav tau: Lub sijhawm nyob hauv huab cua (t)

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (40 m/s)(sin 30^o) = (40 m/s)(0.5) = 20 m / s

Peb xub xam lub sijhawm kom mus txog qhov siab tshaj plaws siv cov qauv ntawm kev txav ntsug.

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 20 m / s (zoo sab saud)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m / s² (tsis zoo downward)

Qhov ceev kawg ntawm qhov siab tshaj plaws (v_t= 0 TZS

Xav tau: Lub sijhawm luv (t)

Tshuaj:

v_t = v_o + gt

0 = 20 + (-10)t

0 = 20 – 10 t

20 = 10 t

t = 20/10 = 2 vib nas this

Lub sijhawm nyob hauv huab cua = 2 x 2 vib nas this = 4 vib nas this.

Lub khoom nyob siab 10 meters saum av. 4 vib nas this yog lub sijhawm kom mus txog qhov chaw uas sib luag rau qhov chaw pib. Lub pob tseem txav mus rau hauv qab.

Lub sijhawm uas yuav mus txog hauv av yog xam los ntawm kev siv cov qauv ntawm kev txav mus los dawb. 

Paub:

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m / s²

Qhov siab (h) = 10 meters

Xav tau: Lub sijhawm luv (t)

Tshuaj:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 t²

t² = 10/5 = 2

t = √2 = 1.4 vib nas this

Lub sijhawm sib nrug = 1.4 vib nas this.

Tag nrho lub sijhawm sib nrug = 4 vib nas this + 1.4 vib nas this = 5.4 vib nas this.

4. Ib lub pob me me uas raug tso tawm kab rov tav nrog qhov ceev pib v_o = 15 m/s ntawm lub tsev siab 5 meters. Xam lub sijhawm nyob saum huab cua! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m / s²

Paub:

Qhov siab (h) = 5 meters

Qhov ceev pib (v_o) = 15 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

SE pob: Lub sijhawm nyob hauv huab cua (t)

Tshuaj:

Lub sijhawm nyob hauv huab cua yog suav los ntawm kev siv cov qauv ntawm kev txav mus los ywj pheej.

Paub:

Qhov siab (h) = 5 meters

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Lub sijhawm luv (t)

Tshuaj:

h = 1/2 gt²

5 = 1/2 (10) t²

5 = 5 t²

t² = 5/5 = 1

t = √1 = 1 vib nas this

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv

Tau daws cov teeb meem hauv kev txav mus los ntawm projectile - txiav txim siab qhov siab tshaj plaws

1. Ib lub pob ncaws pob uas raug ncaws tawm hauv av ntawm lub kaum sab xis θ = 60^o nrog rau kab rov tav muaj qhov pib ceev ntawm 10 m / s. Xam qhov siab tshaj plaws! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 60^o

Qhov ceev pib (v_o) = 10 m/s

Xav tau: Qhov siab tshaj plaws (h)

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

kev txhaum 60^o = v_oy / ua v_o

v_oy = v_o kev txhaum 60^o = (10)(kev txhaum 60^o) = (10)(0.5√3= 5 TZS√3 m / s

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m/s² (tsis zoo downward)

Feem ntsug ntawm qhov ceev pib (v)_oy) = +5√3 m / s (zoo sab saud)

Qhov ceev kawg ntawm qhov siab tshaj plaws (v_ty= 0 TZS

Xav tau: Qhov siab tshaj plaws (h)

Tshuaj:

v_t² = v_o² + 2 gh

0² = (5√3)² + 2 (-10) teev

0 = 25(3) – 20 teev

0 = 75 – 20 teev

75 = 20 h

h = 75 / 20

h = 3.75 meters

Qhov siab tshaj plaws yog 3.75 meters.

2. Ib lub cev raug nthuav tawm rau saum ntuj ntawm lub kaum sab xis ntawm 30^o nrog rau kab rov tav los ntawm lub tsev siab 20 meters. Nws qhov ceev pib yog 4 m/s. Xam qhov siab tshaj plaws! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 30^o

Qhov siab pib (h) = 20 meters

Qhov ceev pib (v_o) = 4 m/s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Qhov siab tshaj plaws (h)

Tshuaj:

Feem ntsug ntawm qhov ceev pib:

kev txhaum 30^o = v_oy / ua v_o

v_oy = v_o kev txhaum 30^o = (4)(kev txhaum 30^o) = (4)(0.5) = 2 m / s

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m/s² (tsis zoo downward)

Feem ntsug ntawm qhov ceev pib (v)_oy) = +2 m / s (zoo sab saud)

Qhov ceev kawg ntawm qhov siab tshaj plaws (v_ty= 0 TZS

Xav tau: Qhov siab tshaj plaws

Tshuaj:

Qhov siab tshaj plaws:

v_t² = v_o² + 2 gh

0² = 2² + 2 (-10) teev

0 = 4 – 20 teev

4 = 20 h

h = 4 / 20

h = 0.2 meters

Qhov siab tshaj plaws yog 0.2 meters + 20 meters = 20.2 meters.

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv

Tau daws cov teeb meem hauv kev txav mus los ntawm projectile - txiav txim siab qhov kev hloov pauv kab rov tav

1. Ib lub pob ncaws pob uas raug ncaws tawm hauv av ntawm lub kaum sab xis θ = 60^o nrog rau kab rov tav muaj qhov ceev pib ntawm 16 m/s. Yuav siv sijhawm ntev npaum li cas ua ntej lub pob ntaus hauv av?

Paub:

Lub kaum sab xis (θ) = 60^o

Qhov ceev pib (v_o) = 16 m / s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: Kev hloov chaw kab rov tav (x)

Tshuaj:

Kab rov tav ntawm qhov ceev pib:

v_ox = v_o cos θ = (16 m/s)(cos 60^o) = (16 m/s)(0.5) = 8 m / s

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (16 m/s)(sin 60^o) = (16 m/s)(0.5√3= 8 TZS√3 m / s

Projectile zog yuav nkag siab los ntawm kev tshuaj xyuas cov khoom kab rov tav thiab ntsug ntawm kev txav mus los sib cais. Kev txav mus los x tshwm sim ntawm qhov ceev tas li thiab kev txav mus los y tshwm sim ntawm qhov nrawm tas li ntawm lub ntiajteb txawj nqus.

Lub sijhawm nyob hauv huab cua

Lub sijhawm uas nws nyob hauv huab cua yog txiav txim los ntawm kev txav ntawm y. Peb xub nrhiav lub sijhawm siv kev txav ntawm y thiab tom qab ntawd siv tus nqi sijhawm no hauv cov kab zauv x (qhov ceev tas li sib npaug).

Xaiv qhov kev taw qhia mus rau sab saud ua qhov zoo thiab qhov kev taw qhia mus rau sab hauv ua qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 8√3 m / s (v_o nce mus rau saum)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m/s² (g nqes mus)

Qhov siab (h) = 0 (lub pob rov qab mus rau tib qho chaw)

Xav tau: Lub sijhawm nyob hauv huab cua

Tshuaj:

h = v_o t + 1/2 gt²

0 = (8√3) t + 1/2 (-10) t²

0 = 8√3 t – 5 t²

8√3 t = 5 t²

8 (1.7) = 5 t

14 = 5 t

t = 14 / 5 = 2.8 vib nas this

Kev hloov chaw kab rov tav

Paub:

Tshaj tawm (v) = 8 m/s

Lub sijhawm luv (t) = 2.8 vib nas this

Xav tau: xaav

Tshuaj:

x = vt = (8 m/s)(2.8 s) = 22.4 meters

Qhov siab ntawm lub tsev yog 22.4 meters.

2. Ib lub cev raug nthuav mus rau saum ntuj ntawm lub kaum sab xis ntawm 60^o nrog rau kab rov tav los ntawm lub tsev siab 50 meters. Nws qhov ceev pib yog 30 m/s. Xam qhov kev hloov chaw kab rov tav! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m/s².

Paub:

Lub kaum sab xis (θ) = 60^o

Qhov siab (h) = 15 m

Qhov ceev pib (v_o= 30 TZS m / s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: x

Tshuaj:

Kab rov tav ntawm qhov ceev pib ::

v_ox = v_o cos θ = (30 m/s)(cos 60^o) = (30 m/s)(0.5) = 15 m/s

Feem ntsug ntawm qhov ceev pib:

v_oy = v_o sin θ = (30 m/s)(sin 60^o) = (30 m/s)(0.5√3= 15 TZS√3 m / s

Lub sijhawm nyob hauv huab cua

Peb xub nrhiav lub sijhawm siv txoj kev txav y thiab tom qab ntawd siv tus nqi sijhawm no hauv cov kab zauv x (kab zauv ceev tas mus li). Xaiv qhov nce mus rau sab saud raws li qhov zoo thiab qhov nqis mus rau sab hauv raws li qhov tsis zoo.

Paub:

Qhov ceev pib (v_o) = 15√3 m / s (zoo sab saud)

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = -10 m/s² (tsis zoo downward)

Siab (h) = -50 (Hauv av 50 meters hauv qab qhov chaw pib)

Xav tau: t

Tshuaj:

h = v_o t + 1/2 gt²

-50 = (15√3) t + 1/2 (-10) t²

-50 = 15√3 t – 5 t²

5 t² - 15√3 t – 50 = 0

Xam lub sijhawm siv cov qauv no:

ib = 5, b = –15√3, c = –50

Lub sijhawm nyob hauv huab cua yog 6.7 vib nas this.

Kev hloov chaw kab rov tav:

Paub:

Qhov ceev (v) = 15 m/s

Lub sijhawm luv (t) = 6.7 vib nas this

Xav tau: xaav

Tshuaj:

s = vt = (15 m/s)(6.7 s) = 100.5 meters

Qhov siab ntawm lub tsev yog 100.5 meters.

3. Ib lub pob me me uas raug tso tawm kab rov tav nrog qhov ceev pib v_o = 10 m/s ntawm lub tsev siab 10 meters. Xam qhov kev hloov chaw kab rov tav! Kev nrawm ntawm lub ntiajteb txawj nqus yog 10 m / s²

Paub:

Qhov siab (h) = 10 m

Qhov ceev pib (v_o= 10 TZS m / s

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Xav tau: x

Tshuaj:

Kab rov tav ntawm qhov ceev pib = qhov ceev pib = 10 m/s.

Lub sijhawm nyob hauv huab cua

Lub sijhawm nyob hauv huab cua suav los ntawm kev siv kev txav mus los dawb kab zauv.

Paub:

Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s²

Qhov siab (h) = 10 meters

Xav tau: t

Tshuaj:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 t²

t² 10/5 = 2

t = √2 = 1.4 vib nas this

Kev hloov chaw kab rov tav

Kev hloov chaw kab rov tav suav los ntawm kev siv kab zauv ntawm kev txav mus los ntawm qhov ceev tas li.

Paub:

Qhov ceev (v) = 10 m/s

Lub sijhawm luv (t) = 1.4 vib nas this

Xav tau: x

Tshuaj:

s = vt = (10 m/s)(1.4 s) = 14 meters

Qhov siab ntawm lub tsev yog 14 meters.

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv

Tau daws cov teeb meem hauv kev txav mus los ntawm projectile - txiav txim siab qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug

1. Ib lub pob ncaws pob uas raug ncaws tawm hauv av ntawm lub kaum sab xis θ = 60^o nrog qhov ceev ntawm 10 m/s. Xam cov khoom pib ntawm qhov ceev!
Paub:
Lub kaum sab xis (θ) = 60^o
Qhov ceev pib (v_o) = 10 m/s
Xav tau: v_ox thiab v_oy
Tshuaj:
Txiav txim siab qhov ceev pib rau hauv x Cheebtsam (kab rov tav) thiab y Cheebtsam (ntsug).
sin θ = v_oy / ua v_o —–> v_oy = v_o sib θ
cos θ = v_ox / ua v_o —–> v_ox = v_o cos θ

x Cheebtsam (kab rov tav):
v_ox = v_o cos θ = (10 m/s)(cos 60^o) = (10 m/s)(0.5) = 5 m/s

y Cheebtsam (ntsug):
v_oy = v_o sin θ = (10 m/s)(sin 60^o) = (10 m/s)(0.5√3) = 5√3 m/s

2. Ib yam khoom tawm hauv av ntawm lub kaum sab xis θ = 30^o nrog y feem ntawm qhov ceev 10 m/s. Xam qhov ceev pib!
Paub:
Lub kaum sab xis (θ) = 30^o
y Cheebtsam (v_oy) = 10 m/s
Xav tau: Qhov ceev pib (v_o)
Tshuaj:
v_oy = v_o sib θ
10 = (v)_o)(kev txhaum 30^o)
10 = (v)_o)(0.5)
v_o = 10/0.5
v_o = 20 m/s

3. Qhov feem ntawm kab rov tav ntawm qhov ceev pib yog 30 m/s thiab qhov feem ntsug ntawm qhov ceev pib yog 40 m/s. Xam qhov ceev pib.
Paub:
Kab rov tav ntawm qhov ceev pib (v)_ox) = 30 m/s
Feem ntsug ntawm qhov ceev pib (v)_oy) = 40 m/s
Xav tau: Qhov ceev pib (v_o)
Tshuaj:
v_o² = v_ox² +v_oy² = 30² + 40² Luas = 900 + 1600 = 2500
v_o = √2500
v_o = 50 m/s

4. Ib lub pob me me raug tso tawm kab rov tav nrog qhov ceev pib v_o = 6m/s. Xam cov x Cheebtsam thiab y Cheebtsam ntawm qhov ceev pib.
Paub:
Qhov ceev pib (v_o) = 6 m/s
Xav tau: lus thiab v_oy
Tshuaj:
Lub pob txav mus rau kab rov tav kom qhov sib txuas ntawm qhov ceev (v)_ox) = qhov ceev pib (v_o) = 6 m/s. Feem ntsug ntawm qhov ceev (v)_oy) = 0.

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1. Txheeb xyuas qhov ceev pib rau hauv cov khoom kab rov tav thiab ntsug
2. Txheeb xyuas qhov kev hloov pauv kab rov tav
3. Txheeb xyuas qhov siab tshaj plaws
4. Txheeb xyuas lub sijhawm sib nrug
5. Txheeb xyuas qhov chaw ntawm cov khoom
6. Txheeb xyuas qhov ceev kawg

nyeem ntxiv