$(a)$ An arrow moves forward when released from a stretched bow. Explain the transformation of energy in the process.
$(b)$ $A$ boy of mass $50 \, kg$ climbs up a vertical height of $100 \, m$. Calculate the amount of potential energy he gains.

$A$ light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

State whether the following statement is true or false:
When velocity is halved,its kinetic energy becomes $\frac{1}{4}^{th}$ of its original value.

Two children $A$ and $B$ each weighing $20 \, kg$ climb a rope up to a height of $10 \, m$. Child $A$ takes $10 \, s$ and child $B$ takes $20 \, s$ to climb. State whether the work done by both is equal or unequal. Who has more power?

$(i)$ An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expression.
$(ii)$ $A$ certain force acting on a $20 \, kg$ mass changes its velocity from $5 \, m s^{-1}$ to $2 \, m s^{-1}$. Calculate the work done by the force.

Can any object have mechanical energy even if its momentum is zero? Explain.