Question

I need help with some math

Answer 1

3.

We can use the projectile motion equations.

Let:

`\begin{gathered} h1(t)=height_{\text{ }}of_{\text{ }}the_{\text{ }}pencil \\ h2(t)=height_{\text{ }}of_{\text{ }}the_{\text{ }}ball \end{gathered}`

Where:

`\begin{gathered} h1(t)=v_(01)t-(1)/(2)gt^2 \\ h1(t)=yf-yi \\ yf-40=35t-(1)/(2)(9.8)t^2 \\ h2(t)=v_(02)t-(1)/(2)gt^2 \\ h2(t)=62.5t-(1)/(2)(9.8)t^2 \end{gathered}`

So, we need to find when:

`yf=h2(t)`

so:

`35t-(1)/(2)(9.8)t^2+40=62.5t-(1)/(2)(9.8)t^2`

Solve for t:

`\begin{gathered} 35t+40=62.5t \\ 62.5t-35t=40 \\ 27.5t=40 \\ t=(40)/(27.5) \\ t\approx1.45s \end{gathered}`

Answer:

The ball and the pencil will have the same height after 1.45 seconds