Falling rock integration problem

[MrJoe2000]

Hi,

I have a problem where I have to calculate the time it takes for a rock to fall from a balloon that is moving downwards with a speed of 15 ft/s from a height of 904 ft.

My answer is 8 seconds but the book is saying 113/16 or 7 and 1/16 seconds.

Which is correct?

 

[soroban]

Hello, MrJoe2000!

I have a problem where I have to calculate the time it takes for a rock to fall from a balloon
that is moving downwards with a speed of 15 ft/s from a height of 904 ft.

My answer is 8 seconds, but the book is saying 113/16 or 7 and 1/16 seconds.

Which is correct?

The book is correct ... sorry!

I bet you misplaced a minus-sign somewhere.


The formula for the rock's height is: .\(\displaystyle h \:=\:h_o + v_ot - 16t^2\)

. . where: .\(\displaystyle \begin{Bmatrix}h_o &=& \text{initial height} \\ v_o &=& \text{initial velocity} \end{Bmatrix}\)


Did you notice that the initial velocity is 15 ft/sec downward?
. . Hence, \(\displaystyle v_o \,=\) -15 ft/sec.