Question

A man is changing a light bulb at the top of a 1500 foot tall radio tower and drops his screwdriver.  Assuming no air resistance, how long will it take to hit the ground in seconds?

Answer 1

Answer:

9.68 seconds

Explanation:

To answer the question, we will use the following equation for the uniformly accelerated motion:

$x=v_0t+\frac{1}{2}at^2$

Where x is the distance travel by the object, v0 is the initial velocity, a is the acceleration and t is the time.

Since, the man drops his screwdriver, x = 1500 ft, v0 = 0 ft/s and a = -32 ft/s².

Then, replacing the values, we get:

$\begin{gathered} -1500=0t+\frac{1}{2}(-32)t^2 \\ -1500=\frac{1}{2}(-32)t^2 \end{gathered}$

Then, solving for t, we get:

$\begin{gathered} -1500=-16t^2 \\ \frac{-1500}{-16}=\frac{-16t^2}{-16} \\ 93.75=t^2 \\ \sqrt[]{93.75}=t \\ 9.68\text{ s = t} \end{gathered}$

Therefore, the screwdriver takes 9.68 seconds to hit the ground.