Grantham PHY220 Week 1 Assignment Problem 8

Problem 8

A stone is dropped from the roof of a high building. A second stone is dropped 1.25 s later. How long does it take for the stones to be 25.0 meters apart?

Solution:

Let t be the amount of time after the first stone is dropped. The distance from traveled by the first stone is

y_1=\frac{1}{2}gt^2

The distance traveled by the second stone is

y_2=\frac{1}{2}g\left(t-1.25\right)^2

The difference between the two stones is 25.0 m after time

y_1-y_2=25.0

\frac{1}{2}\left(9.80\:m/s^2\right)t^2-\frac{1}{2}\left(9.80\:m/s^2\right)\left(t-1.25\right)^2=25

4.9t^2-4.9\left(t^2-2.5t+1.5625\right)=25.0

4.9t^2-4.9t^2+12.25t-7.65625=25.0

12.25t=25.0+7.65625

12.25t=32.65625

t=2.67\:s

 

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