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Basketball shot A basketball is shot at an angle of 45° to the horizontal. The center of the basketball is at the point A(0, 8) at the moment it is released, and it passes through the center of the basketball hoop that is located at the point B(18, 10). Assume the basketball does not hit the front of the hoop (otherwise it might not pass through the basket). The validity of this assumption is investigated in parts (d), (e), and (f ).
a. Determine the initial speed of the basketball.
b. Find the initial velocity v(0) at the moment it is released.
c. Find the position function r(t) of the center of the basketball t seconds after the ball is released. Assume r(0) = ⟨0, 8⟩.
d. Find the distance s(t) between the center of the basketball and the front of the basketball hoop t seconds after the ball is released. Assume the diameter of the basketball hoop is 18 inches.
e. Determine the closest distance (in inches) between the center of the basketball and the front of the basketball hoop.
f. Is the assumption that the basketball does not hit the front of the hoop valid? Use the fact that the diameter of a women’s basketball is about 9.23 inches. (Hint: The ball hits the front of the hoop if, during its flight, the distance from the center of the ball to the front of the hoop is less than the radius of the basketball.)
Kinematic relation for Horizontal displacement
kinematic relation for vertical displacement
(a) Initial speed
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