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

h = 105.98 m

Step-by-step 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 = ( (45.6\ m/s)^2)/(2(9.81\ m/s^2))`

h = 105.98 m