Question

A robot on a basketball court needs to throw the ball in the hoop. The ball have a velocity of 10 m/s and an an angle of 60 degrees. The high of hoop is 0.75 meters and the horizontal distance between the robot and hoop is 5 meters.

A) draw a digram.

B)What is the high that the robot needs to throw the ball from.

Answer 1

a)

v_o = initial velocity of launch = 10 m/s

= angle of launch = 60

Consider the motion of the ball along the horizontal direction

v_ox = initial velocity along x-direction = v_o Cos = 10 Cos60 = 5 m/s

x = horizontal distance between the robot and hoop = horizontal displacement of the ball = 5 m

a_x = acceleration along horizontal direction = 0 m/s²

t = time of travel

Using the equation

x = v_ox t + (0.5) a_x t²

5 = (5) t + (0.5) (0) t²

t = 1 sec

Consider the motion along the vertical direction

Y_o = initial position = height at which the ball is launched

Y = final position = height of the hoop = 0.75 m

v_oy = initial velocity along y-direction = v_o Sin = 10 Sin60 = 8.66 m/s

a_y = acceleration along vertical direction = - 9.8 m/s²

t = time of travel = 1 sec

Using the equation

Y = Y_o + v_oy t + (0.5) a_y t²

Y = 0.75 + (8.66) (1) + (0.5) (- 9.8) (1)²

Y = 4.5 m