# 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/s^{2}. Ignore air resistance.

__Known :__

Initial velocity (v_{o}) = 10 m/s

Time elapsed (t) = 2 seconds

Acceleration of gravity (g) = 10 m/s^{2}

Wanted : Final velocity (v_{t})

__Solution :__

Acceleration 10 m/s^{2 }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 t^{2 }………. 2

v_{t}^{2} = v_{o}^{2} + 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/s^{2}

__Wanted :__ the height of the bridge (h)

__Solution :__

h = v_{o} t + ½ g t^{2}

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/s^{2}

__Wanted :__

(a) Time interval (t)

(b) Final velocity (v_{t})

__Solution :__

(a) Time interval (t)

__Final velocity :__

v_{t}^{2} = v_{o}^{2} + 2 g h

v_{t}^{2} = (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

- Distance and displacement
- Average speed and average velocity
- Constant velocity
- Constant acceleration
- Free fall motion
- Down motion in free fall
- Up and down motion in free fall