Question

A body of mass 0.5 kg with a velocity one-third of its velocity makes a head-on collision with an identical ball. After the collision, the cube moves off with a speed of 2 m/s in the original direction. Calculate the initial velocity of P.

A. 3 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s

Answer 1

Using the conservation of momentum, the initial velocity of the first ball (P) before a head-on collision with an identical stationary ball was calculated to be 3 m/s (option A).

Step-by-step explanation:

Calculating the Initial Velocity of a Colliding Object:

The question involves a collision between two identical balls where one ball with an unknown initial velocity collides head-on with another identical stationary ball. To calculate the initial velocity of the first ball (P), we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocity of ball P as v, the mass of each ball as m, and the final velocity of the first ball after the collision as v'. Since the balls have the same mass and the second ball is at rest before the collision, we can set up the following equation based on the conservation of momentum:

m × v = m × v' + m × (1/3)v

Solving for v, we find that:

v = (m × v' + m × (1/3)v)/m

Since the mass m is the same for both sides of the equation, it cancels out:

v = v' + (1/3)v

Given that v' is 2 m/s (final velocity of the first ball after the collision), we can solve for v:

1 v = 2 m/s + (1/3)v

This simplifies to:

(2/3)v = 2 m/s

And finally:

v = (2 m/s) / (2/3)

v = 3 m/s

Therefore, the initial velocity of ball P is 3 m/s, corresponding to option A.