Answer:
The initial velocity is 0.5114 m/s or 511.4 mm/s
Explanation:
Let the initial velocity be 'v'.
Given:
Mass of the ball (m) = 130 g = 0.130 kg [ 1 g = 0.001 kg]
Initial height of the ball (h₁) = 1.4 mm = 0.0014 m [ 1 mm = 0.001 m]
Final height of the ball (h₂) = 15 mm = 0.015 m
Now, from conservation of energy principle, energy can neither be created nor be destroyed but converted from one form to another.
Here, the kinetic energy of the ball is converted to gravitational potential energy of the ball after reaching the final height.
Change in kinetic energy is given as:
As it just touches the 15 mm high roof, the final velocity will be zero. So,
.
Now, the change in kinetic energy is equal to:
Change in gravitational potential energy = Final PE - Initial PE
So,
[ g = 9.8 m/s²]
Now, Change in KE = Change in PE
Therefore, the initial velocity is 0.5114 m/s or 511.4 mm/s