Down motion in free fall – problems and solutions

Solved Problems in Linear Motion – Down motion in free fall

1. A ball is thrown vertically downward with initial speed 10 m/s and reach the ground in 2 seconds. Find final speed just before the ball hits the ground. Acceleration of gravity (g) = 10 m/s². Ignore air resistance.

Known :

Initial velocity (v_o) = 10 m/s

Time elapsed (t) = 2 seconds

Acceleration of gravity (g) = 10 m/s²

Wanted : Final velocity (v_t)

Solution :

Acceleration 10 m/s² means speed increase by 10 m/s each second. After 3 second, speed = 30 m/s.

Final velocity = 10 m/s + 20 m/s = 30 m/s.

Kinematic equations for motion at constant acceleration, as shown below :

v_t = v_o + a t ………. 1

h = v_o t + ½ a t² ………. 2

v_t² = v_o² + 2 a h ………. 3

v_t = v_o + g t

v_t = 10 + (10)(2)

v_t = 10 + 20 = 30 m/s

Final velocity = v_t = 30 m/s

2. A stone is thrown vertically downward from a bridge with initial speed 5 m/s and reach the water in 2 seconds. Calculate the height of the bridge.

Known :

Initial velocity (v_o) = 5 m/s

Time elapsed (t) = 2 seconds

Acceleration due to gravity (g) = 10 m/s²

Wanted : the height of the bridge (h)

Solution :

h = v_o t + ½ g t²

h = (5)(2) + ½ (10)(2)²

h = 10 + (5)(4)

h = 10 + 20

h = 30 meters

3. A ball is thrown vertically downward with initial speed 10 m/s from a height of 80 meters. Find (a) Time in air (b) Final velocity just before ball strikes the ground.

Known :

height (h) = 80 meters

Initial velocity (v_o) = 10 m/s

Acceleration of gravity (g) = 10 m/s²

Wanted :

(a) Time interval (t)

(b) Final velocity (v_t)

Solution :

(a) Time interval (t)

Final velocity :

v_t² = v_o² + 2 g h

v_t² = (10)² + 2(10)(80) = 100 + 1600 = 1700

v_t = 41 m/s

Time interval (t) :

v_t = v_o + g t

41 = 10 + (10)(t)

41 – 10 = 10 t

31 = 10 t

t = 31 / 10 = 3,1 seconds

(b) Final velocity (v_t) ?

v_t = 41 m/s

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1. Distance and displacement
2. Average speed and average velocity
3. Constant velocity
4. Constant acceleration
5. Free fall motion
6. Down motion in free fall
7. Up and down motion in free fall