Question

A 0.311 kg tennis racket moving
30.3 m/s east makes an elastic
collision with a 0.0570 kg ball
moving 19.2 m/s east. Find the
velocity of the tennis racket after
the collision.

Answer 1

The velocity of the tennis racket after collision is 26.862 m/s.

Explanation:

If the tennis racket and ball is collided in elastic collision then the sum of momentum before collision will be equal to the sum of momentum after collision. This is in accordance to the law of conservation of energy. So if we consider the mass of tennis racket as m1 = 0.311 kg and the velocity of tennis racket before collision as u1 = 30.3 m/s. Then the mass of the ball is considered as m2 = 0.0570 kg and the velocity of the ball before collision as u2 = 19.2 m/s.

So as per the conservation of energy, the velocity of tennis racket and ball after collision will be denoted as v1 and v2 respectively. The formulas for determining these velocities are

$v_{1} = \frac{m_{1}- m_{2} }{m_{1} + m_{2} } u_{1}+ \frac{ 2*m_{2} }{m_{1} + m_{2} } u_{2}$

$v_{2} = \frac{2*m_{1} }{m_{1} + m_{2} } u_{1}+ \frac{ m_{2}- m_{1} }{m_{1} + m_{2} } u_{2}$

Since, we require to determine only the velocity of tennis racket after collision, so solving the v1 equation is enough with the parameters m1 = 0.311 kg , m2 = 0.0570 kg, u1 = 30.3 m/s and u2 = 19.2 m/s given

$v_{1} = \frac{0.311- 0.0570 }{0.311 + 0.0570 } * 30.3+ \frac{ 2*0.0570 }{0.311 + 0.0570 }*19.2$

$v_{1} = \frac{0.254 }{0.368} * 30.3+ \frac{ 0.114 }{0.368}*19.2$

$v_{1} =20.914+5.948=26.862 m/s$

So, the velocity of the tennis racket after collision is 26.862 m/s.

Answer 2

Answer:

The velocity of the tennis racket after the collision 14.966 m/s.

Explanation:

Step-by-step explanation:

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

let the following:

m₁ = mass of tennis racket = 0.311 kg

m₂ = mass of the ball = 0.057 kg

u₁ = velocity of tennis racket before collision = 30.3 m/s

u₂ = velocity of the ball before collision = -19.2 m/s

v₁ = velocity of tennis racket after collision

v₂ = velocity of the ball after collision

Right (+) , Left (-)

v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

= ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)

= 14.966 m/s.

So, the velocity of the tennis racket after the collision 14.966 m/s