Question

A wooden block of mass 20g is dropped from the top of the cliff 50 m high. Simultaneously a bullet of mass 20 g is fired from the foot of the cliff upwards with a velocity 25 ms. The bullet and the wooden block will meet each other after time:

Answer 1

Hint: In this question, we will use the third equation of motion, which gives us relation between the distance travelled, initial velocity, time and acceleration. Further, on finding the values, we put them in this equation of motion. This will give us the required result. Also, for better understanding we will know the basics of force and laws of motion given by Newton.

Formula used:
${s_r} = {u_r}t + \dfrac{1}{2}{a_r}{t^2}$

Complete step by step solution:
As we know that there are three equations of motion given by Newton. These equations help us find different physical quantities like initial velocity, final velocity, time, distance and acceleration.
Here, we first find the resultant initial velocity, which is given by:
${u_r} = {u_2} - {u_1}$
$\eqalign{& \Rightarrow {u_r} = 25 - 0 \cr
  & \Rightarrow {u_r} = 25m/s \cr} $
Now, we find the resultant acceleration, which is given by:
${a_r} = {a_2} - {a_1}$
$\eqalign{& \Rightarrow {a_r} = - 9 - ( - 9) \cr
  & \Rightarrow {a_r} = 0 \cr} $
Now, we use the third equation of motion to further find the value of the time when the bullet and the wooden block will meet each other.
${s_r} = {u_r}t + \dfrac{1}{2}{a_r}{t^2}$
By, substituting the values in the above equation we get:
$\eqalign{& 50 = 25 \times t + 0 \cr
  & \Rightarrow t = \dfrac{{50}}{{25}} \cr
  & \therefore t = 2\sec \cr} $
Therefore, we get the required time at which both the wooden block and the bullet will meet, which is given by the above result.

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: We should remember that the equations of motion are applicable to classical bodies or systems only; these are not applicable in quantum mechanics. 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.