Question

Steph is taking 3-point shots 7.3 m away from the 3.05 m tall basket. It thebasketball is released from a height of 1.9 m with an initial velocity of 8.9 m/s [45°above the horizontal, does he make the shot? If not, how should Steph adjust the shot?

Answer 1

Given:

The range of the throw, x=7.3 m

The height of the basket, h=3.05 m

The height from which the ball was thrown, h_i=1.9 m

Initial velocity of the ball, u=8.9 m/s

The angle of projection of the ball, θ=45°

To find:

Does Steph make the shot?

Step-by-step explanation:

The time it takes for the ball to cover a horizontal distance of 7.3 m is given by,

`t=(x)/(u\cos\theta)`

On substituting the known values,

`\begin{gathered} t=(7.3)/(8.9*\cos45\degree) \\ =1.16\text{ s} \end{gathered}`

The height of the ball when the ball is at a horizontal distance of 7.3 m is given by,

`h_f=u\sin\theta t-(1)/(2)gt^2+h_i`

Where g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} h_f=8.9*\sin45\degree*1.16-(1)/(2)*9.8*1.16^2+1.9 \\ =2.6\text{ m} \end{gathered}`

Final answer:

Thus Steph will not make the shot.

To make the shot Steph either have to decrease the velocity with which he throws the ball or increase the angle of projection of the ball.