Question

A certain freely falling object, released from rest, requires 1.35 s to travel the last 38.5 m before it hits the ground.

(a) Find the velocity of the object when it is 38.5 m above the ground. (Indicate the direction with the sign of your answer. Let the positive direction be upward.)

m/s

(b) Find the total distance the object travels during the fall.

Answer 1

Given: s = displacement = 38.5m
t = 1.35s
Vo = ?
a = 9.8 m/s^2

a) Using the following formula for free-fall motion:

s = Vo*t + (1/2)a*t^2
38.5 = Vo * 1.35 + (1/2)(9.8)*1.35^2
Vo = -21.9 m/s

b) Solving for the distance prior to reaching 38.5m before reaching the ground:

Vf = Vo + at

Where:
Vf = 21.9 m/s
Vo = 0
a = 9.8
t = ?

21.9 = 0 + (9.8)*t
t = 2.24s

Solving for s:

s = (Vo + Vf)/2 *t
s = (0 + 21.9)/2 * 2.24
s = 24.528 m

Solving for the total displacement:

Total displacement = 24.528 m + 38.5 m
Total displacement = 63.028 m