Question

A ball of mass m is released from rest at a distance h above a friction less plane inclined at an angle of 45° to the horizontal as shown above. The ball bounces horizontally off the plane at point P₁ with the same speed with which it struck the plane and strikes the plane again at point P₂ In terms of g and h determine each of the following quantities:

 

a. The speed of the ball just after it first bounces off the plane at P₁. 

b. The time the ball is in flight between points P₁ and P₂. 

c. The distance L along the plane from P₁ to P₂. 

d. The speed of the ball just before it strikes the plane at P₂.  

Answer 1

a. The speed after falling a height h is found from

Comments

Why is L over the square root of 2? Is there particular trig involved?

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The horizontal distance between P_1 and  P_2 = Lcos 45°= L/√2