  A basketball player attempts a three-point shot 10.0 m from the basket as shown in the figure below. The player shoots the ball at an angle ofθ = 36.4° from horizontal, and releases the ball at a height of h = 2.20 m. The rim of the basket is at a height of H = 3.05 m.At what speed (in m/s) must the player throw the basketball so that the ball goes through the hoop without striking the backboard?

Question

A basketball player attempts a three-point shot 10.0 m from the basket as shown in the figure below. The player shoots the ball at an angle of
θ = 36.4° from horizontal, and releases the ball at a height of h = 2.20 m. The rim of the basket is at a height of H = 3.05 m.
At what speed (in m/s) must the player throw the basketball so that the ball goes through the hoop without striking the backboard?

Step 1

Given,

Horizontal displacement, x = 10 m

Vertical displacement, y = (3.05 -2.2) = 0.85 m

Angle of shoot, θ  = 36.4o

Step 2

Formula used.

Where,

y = vertical position (m)

x = horizontal position (m)

v0 = initial velocity (combined components, m/s)

g = acceleration due to gravity (9.80 m/s2)

θ = angle of the initial velocity from the horizontal plane (radians or degrees)

Step 3

Form the equation of traje...

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