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Determine the distance when the ball is struck again

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A ball of mass 150 g is fired from a smooth 30 degree incline at an angle theta with the incline as shown in the figure in the attachment. The initial velocity of the ball is v0 = 10 m/s. It travels after struck by the ground with the velocity v2 as shown. If the coefficient of restitution between ball and ground is 0.75, determine the distance d when the ball is again struck by the ground. Also calculate the time t when the ball struck the ground for the second time.

Please show all work and solve it just for theta = 30 degrees.

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Solution Preview

Please refer to the attachment.


30O vo = 10 m/s

x1=d1cos30O y1= d1sin30O

v1y v1
y α

As θ = 30O, the ball is projected horizontally (as inclination of the ground is also 30O) with an initial speed of 10 m/s (initial vertical component of velocity is zero).

As the ball is a projectile, its horizontal velocity will remain constant at 10 m/s (neglecting air friction). However, vertical velocity will increase starting from zero.

Further, horizontal displacement when the ball hits the ground = x1 = d1cos30O = ...

Solution Summary

This solution helps determine the distance when the ball is struck by the ground.