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.
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Answer 1

Answer:

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

Step-by-step 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