# Math Help - free fall

1. ## free fall

At time t = 0 s, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. Figure 2-25 gives the vertical positions y of the apples versus t during the falling, until both apples have hit the roadway. With approximately what speed is apple 2 thrown down?

2. Originally Posted by BiGpO6790
[IMG]file:///C:/Users/Nick/AppData/Local/Temp/moz-screenshot-3.jpg[/IMG]At time t = 0 s, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. Figure 2-25 gives the vertical positions y of the apples versus t during the falling, until both apples have hit the roadway. With approximately what speed is apple 2 thrown down?
Take the origin to be the release point, and $y$ positive downwards.

The time it takes the first apple to reach the roadway tells you how high the roadway is. Since for this the distance from the release point is:

$y=gt^2/2$

and we know that $t=2$ seconds when $y$ is the bridge height.

For the second apple we know that the time to hit the road is $1.25$ seconds. The apples distance from the release point is:

$y=gt^2/2 + v_0t$

where t is the time from release of the second apple.

As we know the height of the bridge we set this to $y$, and the time of fall which we set to $t$ we can now solve for the speed with which the apple is thrown down $v_0$

CB