E hoʻoholo i ka wikiwiki hope loa o ka neʻe ʻana o ka projectile

1. A kicked football leaves the ground at an angle θ = 30^o to the horizontal with an initial speed of 14 m/s. Calculate the final velocity before the ball hits the ground.

ʻIke ʻia:

Kihi (θ) = 30^o

Initial velocity (v_o) = 14 m/s

Ka wikiwiki o ke koʻikoʻi (g) = 10 m / s²

Makemake ʻia: Final velocity before the ball hits the ground

Lōlā:

Horizontal component of initial velocity :

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

Vertical component of initial velocity :

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

Final velocity at vertical direction

Choose upward direction as positive and downward direction as negative.

ʻIke ʻia:

Ka wikiwiki mua (v_o) = 7 m/s (positive upward)

Acceleration of gravity (g) = –10 m / s² (negative downward)

Height (h) = 0 (object back to initial position)

Makemake ʻia: Ka wikiwiki hope loa (v_t)

Lōlā:

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

v_t = √49 = 7 m/s

Final velocity at horizontal direction

Initial velocity at horizontal direction is 7√3 m/s. Velocity is constant so that final velocity is same as initial velocity.

Final velocity before the object hits the ground

2. A body is projected upward at an angle of 30^o with the horizontal from a building 5 meter high. Its initial speed is 10 m/s. Calculate final velocity before the object hits the ground! Acceleration of gravity is 10 m/s².

ʻIke ʻia:

Kihi (θ) = 30^o

Ke kiʻekiʻe mua (h_o) = 5 mika

Ka wikiwiki mua (v_o) = 10 m/s

Ka wikiwiki o ke koʻikoʻi (g) = 10 m/s²

Makemake ʻia: Final velocity

Lōlā:

Horizontal component of initial velocity :

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

Vertical component of initial velocity :

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

Final velocity at vertical direction

ʻIke ʻia:

Ka wikiwiki mua (v_o) = 5 m/s (positive upward)

Acceleration of gravity (g) = –10 m / s² (negative downward)

Height (h) = -5 m (negative because the ground is below the initial height)

Makemake ʻia: Ka wikiwiki hope loa (v_t)

Lōlā:

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

v_t = √125 m/s

Final velocity at horizontal direction

Final velocity at horizontal direction is 5√3 m/s.

Final velocity

3. A small ball projected horizontally with initial velocity v_o = 8 m/s from a building 12 meters high. Calculate final velocity before ball hits ground! Acceleration of gravity is 10 m/s²

ʻIke ʻia:

Kiʻekiʻe (h) = 12 mika

Ka wikiwiki mua (v_o) = 8 m/s

Ka wikiwiki o ke koʻikoʻi (g) = 10 m/s²

Makemake ʻia: Ka wikiwiki hope loa (v_t)

Lōlā:

Horizontal component of initial velocity :

v_ox = v_o = 8m/s

Vertical component of initial velocity :

v_oy = 0m/s

Final velocity at vertical direction

calculated using equation of free fall motion.

ʻIke ʻia:

Acceleration of gravity (g) = 10 m / s²

Kiʻekiʻe (h) = 12 m

Makemake ʻia: Ka wikiwiki hope loa (v_t)

Lōlā:

v_t² = 2 gh = 2(10)(12) = 240

v_t = √240 m/s

Final velocity at horizontal direction

Initial velocity at the horizontal direction is 8 m/s. Velocity is constant so that the initial velocity equals the final velocity. So final velocity at horizontal direction is 8 m/s.

Final velocity

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1. E hoʻoholo i ka wikiwiki mua i nā ʻāpana ākea a me ke kū
2. E hoʻoholo i ka neʻe ʻana o ka ʻaoʻao
3. E hoʻoholo i ke kiʻekiʻe loa
4. E hoʻoholo i ka wā ma waena
5. Determine the position of the object
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