Question

The Westin Stamford Hotel in Detroit is 228m tall. If a worker on the roof drops a sandwich, how long does it take the sandwich to hit the ground, assuming there is no air resistance? How would air resistance affect the answer?

Answer 1

Height of the hotel room is given as

$H = 228 m$

now as it falls freely from the top

its initial speed is given as

$v_i = 0$

also the acceleration is given as

$a = g = 9.8 m/s^2$

now we will use kinematics here

$d = v_i*t + \frac{1}{2}at^2$

$228 = 0 + \frac{1}{2}*9.8*t^2$

$228 = 4.9 t^2$

$t^2 = 46.53$

$t = 6.82 s$

so it will take t = 6.82 s to reach the bottom