Question

A ball of mass 400 gm is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 N so that it attains a vertical height of 20 m. The time for which the ball remains in contact with the bat is:

Answer 1

In this question, we will first use the relation between velocity, height and gravity. Further, we will use this result to get the time for which the ball remains in contact with the bat. Also, we will discuss the basics of force and the laws of motion.

Formula used:
$\Rightarrow \Delta p = 12kgm/s$
$\Delta p = m(v + u)$

Complete answer:
The velocity of the ball after dropping from height 5m is given by:
${u^2} = 2g{h_1}$
Substituting the values in the above equation we get:
\eqalign{& \Rightarrow u = \sqrt {2 \times 10 \times 5} \cr & \Rightarrow u = 10m/s \cr} downwards
Now, velocity of ball after being hit by the bat is given by:
${v^2} = 2g{h_2}$
Substituting the values in the above equation we get:
\eqalign{& \Rightarrow v = \sqrt {2 \times 10 \times 20} \cr & \Rightarrow v = 20m/s \cr} Upwards
Further, change in momentum can be calculated as:
$\Delta p = m(v + u)$
Now, by substituting the values in the above equation we get
\eqalign{& \Rightarrow \Delta p = 0.4(10 + 20) \cr & \Rightarrow \Delta p = 0.4 \times 30 \cr}
$\Rightarrow \Delta p = 12kgm/s$
So, from the above result we can also give force F, which can be given as:
$F = 100N = 12/t$
Now, the time of contact t can be given as:
$t = 0.12\sec$
Therefore, we get the required result of the time for which the ball comes in contact with the bat.

Additional information:
Force is simply any push or pull. The S.I unit of force is Newton represented by N. The acceleration is defined as the increase in the velocity of an object. The acceleration is measured in meters per Second Square.
There are three laws of motions given by Newton. These laws of motion relate an object's motion to the forces acting on it.
First law of motion states that an object continues to be in rest or in motion in a particular direction until and unless any external force is applied on it.
In the second law of motion, the force on an object is equal to its mass times its acceleration. This law also gives the relation of momentum and force.
In the third law of motion, every action has an equal and opposite reaction.

Note:
Force applied on an object changes its motion, speed, direction and also its shape. There is a very small difference between the force applied and the pressure applied on an object. Pressure is always given as the force per unit area.