Kinematics Motion

Question

In the 1970 National Basketball Association championship, Jerry West made a 60 ft shot from beyond half court to lead the Los Angeles Lakers to an improbable tie at the buzzer with the New York Knicks. Suppose West threw the ball at an angle of 40∘ above the horizontal. The basket is 10ft from the court floor.

 Neglecting air resistance, estimate the initial speed 𝑣0 of the ball.

Answer 1

Let D = 60 ft. Let H = 10 ft. Let θ = 40°. Let t = time to reach basket. g = 32 fts^-2.

Make the simplifying assumption that the ball is thrown at floor level as we don’t know the height at which the ball is launched.

The equation to determine how long it takes the ball to reach the height of the basket is

H = V sin θ t – ½ g t². There are two unknowns V and t.

The horizontal distance to the basket is D = V cosθ t. This also has two unknowns.

Solve the last equation for t and substitute into the first equation.

H = Vsinθ D/VCosθ – ½ g D² / V² cos²θ. Substitute known values and solve for V.

10 = 60 tan 40 – ½ 32 x 3600 / V² cos² 40.

10 – 60 tan 40 = -98126 / V².

-40.3 = -98126 x 1/V².

V² = 2.43 x 10³

V = 49.3 ft/s

I left out units in the calculation to make the equations more compact. Check math.