Question

2. Washington & Cormick are in the fourth quarter of a basketball game both with 15 points. Washington has a free-throw shot at a horizontal range of 4.52 meters away from the basket. If the player takes a deep breath and calculates her initial velocity to be 6 m/s at an angle of 60 degrees, do they make the shot? In other words, at the peak of the arc will the ball travel high enough to reach the 1.37 meter high hoop.

Answer 1

In order to determine if the shot is made, consider that the ball describes a parabolic motion.

Then, use the following formula for the maximum height reached by the ball:

$h_{\max }=\frac{v^2_o\sin ^2\theta}{2g}$

where, in this case:

vo: intial speed of the ball = 6m/s

θ: launch angle = 60

g: gravitational acceleration constant = 9.8m/s^2

Replace the previous values of the parameters into the formula for the maximum height:

$h_{\max }=\frac{(6\frac{m}{s})^2(\sin 60)^2}{2(9.8\frac{m}{s^2})}\approx1.377m$

As you can notice, the previous result is a little higher than the height of the hoop, then, you can conclude that the ball will travel high enough to reach the hoop.

Now, consider that the horizontal distance traveled by the ball when it reaches the maximum height is:

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