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. Whakaterenga na te kaha o te kaha (g) = 10 m/s².

otinga

We use one of these kinematic equations for motion at constant acceleration, e whakaaturia ana i raro ake nei.

v_t = v_o + i

s = v_o t + ½ i²

v_t² = v_o² + 2 ngā toki

Mōhiotia:

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

Te tere tīmatanga (v_o) = 20 m/s (positive upward)

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

Te tere whakamutunga (v_t) = 0 (it’s speed is zero for an instant at highest point)

E hiahiatia ana: Maximum height (h)

Rongoā:

v_t² = v_o² + 2 g h

0 = (20²) + 2(-10) h

0 = 400 – 20 h

400 = 20 hāora

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/s²Kaua e aro ki te ātete hau.

Mōhiotia:

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

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

tuatahi tere (v_o) = 20 m/s (positive upward)

Acceleration of gravity (g) = -10 m/s² (kino ki raro)

E hiahiatia ana:

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

(b) Final velocity (v_t)

Rongoā:

(a) Te wā (t)

Mōhiotia:

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

Te tere tīmatanga (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

-5 t² + 20 t + 100 = 0

We use quadratic formula :

(b) Final velocity

v_t² = v_o² + 2 g h

v_t² = (20²) + 2 (-10)(-100)

v_t² = 400 + 2000

v_t² = 2400

v_t = 49m/s

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