A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown. The ball enters the basket 0.96 s after it is launched. What are the distances x and y? Note: The drawing is not to scale. x y
A)5.4 m 0.73 m
B)7.7 m 0.91 m
C)5.4 m 0.91 m
D)5.7 m 0.73 m
E)5.4 m 5.4 m

Question

A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown. The ball enters the basket 0.96 s after it is launched. What are the distances x and y? Note: The drawing is not to scale.  x y
A)5.4 m 0.73 m 
B)7.7 m 0.91 m 
C)5.4 m 0.91 m 
D)5.7 m 0.73 m 
E)5.4 m 5.4 m

Quizplus · Accepted Answer

Using the kinematic equations:
Vertical motion (y-axis):
y = vt + 1/2at^2
where y = 0.91 m (height of the basket), v = 8.0 m/s (initial velocity), and t = 0.96 s (time of flight).
0.91 m = (8.0 m/s)(0.96 s) + 1/2(9.81 m/s^2)(0.96 s)^2
0.91 m = 7.68 m + 4.72 m
0.91 m = 12.4 m
Therefore, the vertical distance traveled is 0.91 m.

Horizontal motion (x-axis):
x = vt
where x is the horizontal distance traveled, v is the initial velocity, and t is the time of flight (0.96 s).
x = (8.0 m/s)(0.96 s)
x = 7.68 m
Therefore, the horizontal distance traveled is 7.68 m.
The answer is (C) 5.4 m 0.91 m.

A Basketball Is Launched with an Initial Speed of 8