Answer:
13.08 m/s
Step-by-step explanation:
Coefficient of restitution = (speed of seperation)/(speed of approach)
= (v₁ - v₂)/(u₂ - u₁)
where v₁ = final velocity of the rock = ?
v₂ = final velocity of the inclined plane = 0 m/s
u₂ = initial velocity of the inclined plane = 0 m/s
u₁ = initial velocity of impact of the rock = ?
We can calculate the initial velocity of impact of the rock from the laws of conservation of energy.
Potential energy at the highest height for the rock = kinetic energy at impact
mgh = (1/2)mu₁²
u₁ = √(2gh)
u₁ = √(2×9.8×20) = 19.8 m/s
Using the convention of toward velocity to be negative and upward velocity to be positive.
u₁ = - 19.8 m/s
0.2 = (v₁ - 0)/(0 - (-19.8)]
v₁ = 0.2 × 19.8 = 3.96 m/s
This is the velocity after impact if it were a level surface, calculating for the inclined plane,
The components of the velocity of the rock after impact will be perpendicular to the surface of the inclined plane and parallel to the inclined plane
The component perpendicular to the plane = v₁cos 40° = 3.96 × cos 40° = 3.03 m/s
The component parallel to the plane = u₁ sin 40° = 19.8 × sin 40° = 12.73 m/s
v = √[12.73² + 3.03²] = 13.08 m/s
Hope this Helps!!!