- #1

- 264

- 0

## Homework Statement

A stone is dropped from the top of a 400 m tower. (Acceleration due to gravity is -9.8 m/s2. Ignore air resistance. Give your answers correct to two decimal places.)

## Homework Equations

## The Attempt at a Solution

so part a asks for an equation to model the position of the ball which is:

[tex] h(x)= \frac {-9.8t^{2}}{2}+400 [/tex]

which is correct, the next question asks how long does it take to hit the ground:

[tex] h(x)= \frac {-9.8t^{2}}{2}+400=0 [/tex]

[tex] \frac {-9.8t^{2}}{2}=-400 [/tex]

[tex] -9.8t^{2}=-800 [/tex]

[tex] t^{2}= \frac {4000}{49} [/tex]

[tex] t= \sqrt{ \frac{4000}{49}} \approx 9.04s [/tex]

9.04s is also correct, so the next question asks at what speed does the ball hit the ground, so i take the derivative of h(x) to find this, correct?

[tex] h'(x) = -9.8t [/tex]

[tex] h'(x) = -9.8(9.04) \approx -88.592 \approx -88.6 [/tex]

but i have tried -88.6, -88.59, 88.6, and 88.59 so did I do something wrong here? I must be missing something...

thanks!