Question

If you dropped a ball off the roof, and could neglect air resistance, the impact velocity of the ball on the sidewalk would be 102 miles per hour [mph]. Calculate the height of the building in units of feet.

Answer 1

Answer:

h = 105.98 m

Explanation:

We will use the third equation of motion here:

$2gh= v_f^2-v_i^2$

where,

g = acceleration due to gravity = 9.81 m/s²

h = height = ?

vf = final speed = (102 mi/h)(1 h/3600 s)(1609.34 m/1 mi) = 45.6 m/s

vi = initial speed = 0 m/s

Therefore,

$2(9.81\ m/s^2)h = (45.6\ m/s)^2-(0\ m/s)^2\\\\h = \frac{ (45.6\ m/s)^2}{2(9.81\ m/s^2)}$

h = 105.98 m