Question

In the video, I drop a ball off a three-story balcony. We know that objects in freefall follow the equation for height h, in

meters, h = – 4.9t' + c, where t is time in seconds, and is the initial height. A student timed the drop at 1.27
seconds.
Use this to determine the height from which the ball was dropped, to at least 2 decimal places.
​

Answer 1

The initial height from which the ball was dropped = 7.90 meters

Explanation:

The correct question is:

In the video, I drop a ball off a three-story balcony. We know that objects in free fall follow the equation for height h, in meters,
`h = -4.9t^2 + c`, where
`t` is time in seconds, and
`c` is the initial height. A student timed the drop at 1.27 seconds.

Use this to determine the height from which the ball was dropped, to at least 2 decimal places.

Solution:

The height
`h` of the free falling ball is represented by the equation as:

`h=-4.9t^2+c` where
`t` is time in seconds, and c is the initial height.

To determine the initial height from which the ball was dropped.

The drop was timed at 1.27 seconds, we will plugin
`t=1.27` in the given height function to find
`h(1.27)`

`h(1.27)=-4.9(1.27)^2+c`

`h(1.27)=-7.90+c`

Since, the drop is timed at 1.27 seconds, so in the given time the ball will reach the ground, making
`h(1.27)=0`

So, we have.

`0=-7.90+c`

Adding both sides by 7.90 to solve for
`c`.

`0+7.90=-7.90+7.90+c`

`7.90=c`

∴
`c=7.90\ m`

Thus, the initial height from which the ball was dropped = 7.90 meters