Up and down motion in free fall – problems and solutions

Solved Problems in Linear Motion – Up and down motion in free fall

1. A person throws a ball upward into the air with an initial velocity of 20 m/s. Calculate how high it goes. Ignore air resistance. Paātrinājums gravitācijas dēļ (g) = 10 m/s².

Šķīdums

We use one of these kinematic equations for motion at constant acceleration, kā parādīts zemāk.

v_t = v_o + plkst.

s = v_o t + ½ pie²

v_t² = v_o² + 2 asis

Zināms:

We choose the upward direction as positive and downward direction as negative.

Sākotnējais ātrums (v_o) = 20 m/s (positive upward)

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

Galīgais ātrums (v_t) = 0 (it’s speed is zero for an instant at highest point)

Meklē: Maksimālais augstums (h)

šķīdums:

v_t² = v_o² + 2 gh

0 = (20²) + 2(-10) h

0 = 400 – 20 h

400 = 20 stundas

h = 400 / 20 = 40 / 2 = 20 meters

2. A person throws a stone upward at 20 m/s while standing on the edge of a cliff, so that the stone can fall to the base of the cliff 100 meters below.

(a) How long does it take the ball to reach the base of the cliff (b) Final velocity just before stone strikes the ground. Acceleration due to gravity (g) = 10 m/s²Ignorējiet gaisa pretestību.

Zināms:

We choose the upward direction as positive and downward direction as negative.

High (h) = -100 meters (negative because final position below initial position)

Sākuma ātrums (v_o) = 20 m/s (positive upward)

Brīvās krišanas paātrinājums (g) = -10 m/s² (negatīvs uz leju)

Meklē:

(a) Time in air or time interval (t)

(b) Final velocity (v_t)

šķīdums:

(a) Laika intervāls (t)

Zināms:

High (h) = -100 meters (negative because final position below initial position)

Sākotnējais ātrums (v_o) = 20 m/s (positive upward), Acceleration of gravity (g) = -10 m/s² (negative downward).

h = v_o t + ½ gt²

-100 = (20) t + ½ (-10) t²

-100 = 20 t – 5 t²

-5t² + 20 t + 100 = 0

We use quadratic formula :

(b) Final velocity

v_t² = v_o² + 2 gh

v_t² = (20²) + 2 (-10)(-100)

v_t² = 400 + 2000

v_t² = 2400

v_t = 49m/s

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1. Attālums un pārvietojums
2. Vidējais ātrums un vidējais ātrums
3. Pastāvīgs ātrums
4. Pastāvīgs paātrinājums
5. Brīvā kritiena kustība
6. Kustība uz leju brīvā kritienā
7. Kustība augšup un lejup brīvā kritienā