Question

Will the ball fly over the glove of another 30 feet away trying to catch a ball?

Answer 1

It is given that the height of the baseball is:

`y=-0.1x^2+3x+6`

Where x is the horizontal distance from where the ball was thrown.

It is required to determine if the ball will fly over the glove of another child 30 feet away given that he holds a glove at a height of 5 feet.

To do this, find the height of the baseball 30 feet away from where it was thrown. If the height is greater than 5 feet, it means the ball will fly over the glove which is at a height of 5 feet.

Substitute x=30 into the given equation to find the height of the ball at 30 feet away:

`\begin{gathered} y=-0.1(30)^2+3(30)+6 \\ \Rightarrow y=\left(−0.1\right)\left(900\right)+\left(3\right)\left(30\right)+6 \\ \Rightarrow y=−90+\left(3\right)\left(30\right)+6 \\ \Rightarrow y=−90+90+6 \\ \Rightarrow y=0+6=6 \end{gathered}`

This means that the height of the ball 30 feet away is 6 feet.

Since the height of the ball (6 feet) is greater than the height of the glove (5 feet), it follows that the ball will fly over the glove of another child 30 feet away.

The ball will fly over the glove of another child 30 feet away.