A Boston Celtics basketball player who is 2.00 m tall is standing on the floor L

Question

A Boston Celtics basketball player who is 2.00 m tall is standing on the floor L = 8.00 m from the basket, as in Figure P4.54. If he shoots the ball at a 32.0° angle with the horizontal, at what initial speed must he throw so that it goes through the hoop without striking the backboard? The basket height is 3.05 m. Hints: The ending height is not the same as the starting height, so you cannot use the range or time of flight formulas. Decompose the motion into x and y components. Using the x-component of the motion, write an expression that relates v0 and t. Then do the same for the y-component of motion. You should then have two equations for the two unknowns v0 and t.

Explanation / Answer

t = 8 / Vcos32
t = 9.43/ V
V = 9.43/ t

Now you just need to find the time it took.

1.05 = 0.5(-9.8) (t^2) + Vsin32 (8/ Vcos32)
The V's cancel out, so sin32 * 8 / cos32 = 4.999

1.05 = -4.9(t^2) +4.999
-3.949 = -4.9(t^2)
0.9 = t

Now substitute t into the equation above

V = 9.43 / t
V = 9.43 /0.9
V = 10.5 m/s

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