Question

a ball 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?

Answer 1

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:
`s= (1)/(2) gt^2` 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=
`√(8)=2 √(2) =2.82 sec.`.

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