Question

if the dolphin is moving horizontally when it goes through the hoop how high above the water is the center of the hoop

Answer 1

We are given that a dolphin moves describing a projectile motion. This can be represented in the following graph of position vs time:

Since the dolphin moves horizontally as he goes through the hoop this means that the hoop is at the maximum height of the motion. The maximum height of a projectile motion is given by:

`h_(\max )=(v^2\sin ^2\theta)/(2g)`

Where:

`\begin{gathered} h_(\max )=\text{ max}imum\text{ height} \\ v=velocity_{} \\ \theta=\text{ initial angle} \\ g=\text{ acceleration of gravity} \end{gathered}`

Now, we plug in the values:

`h_{\text{max}}=((10(m)/(s))^2(\sin (41))^2)/(2(9.8(m)/(s^2)))`

Solving the operations:

`h_(\max )=2.2m`

Therefore, the hoop is at 2.2 meters above the water.