Aball is dropped from a height of 120 meters. if it takes 2.00 seconds for a ball to fall 60 meters, how long will it take the ball to reach the ground?

We know that the ball falls under the influence of gravity. Hence, we can assume that its motion is with constant acceleration and it is in a line.
The equation for this kind of motion is:   where s is the distance and g is the acceleration. Since we know that for t=2 sec, s=60m, we can find the acceleration g. Substituting, we get: 60= g*(1/2)*2*2 hence g=30m/s^2 (these are the units of acceleration).

Now, we need to find the time in which the ball drops 120 m. So we substitute s=120m and we know the acceleration. We get then:
120=30/2 *t^2.
Hence, solving for t^2, 240/30=t^2, t^2=8. We get that t=.

It is interesting to notice, that while the distance has doubled, the time has not; the time has only gotten larger by a factor of 1.4

 

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