Question

A 45.0 g golf ball moves to the right 273 km/h and strikes another ball at rest. they collide elastically and the golf ball moves to the left 91 km/h . If the other ball moves 182 km/h to the right, what is its mass?

Answer 1

Answer: M2 = 90g

Therefore, the mass of the other ball is 90g

Step-by-step explanation:

According to the law of conservation of momentum.

M1U1 + M2U2 = M1V1 + M2V2 .....1

Where,

M1 and M2 are mass of golf ball and another ball

U1 and U2 are their initial velocities

V1 and V2 are their final velocities

From equation 1

M1U1 - M1V1 = M2V2 - M2U2

M1U1 - M1V1 = M2V2 - M2U2

M2 = (M1U1 - M1V1)/(V2-U2) .....2

Given;

M1 = 45g

U1 = 273km/h

V1 = -91km/h. (It moves to opposite direction)

U2 = 0

V2 = 182km/h

Substituting into eqn 2

M2 =(45×273 - 45 × -91)/(182-0)

M2 = 16380/182

M2 = 90g

Therefore, the mass of the other ball is 90g

Answer 2

The mass of the other ball = 90 g

Step-by-step explanation:

From the law of conservation of momentum,

Total momentum before collision = total momentum after collision

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where m₁ = mass of the golf ball, m₂ = mass of the other ball, u₁ = initial velocity of the gulf ball, u₂ = initial velocity of the other ball, v₁ = final velocity of the gulf ball, v₂ = final velocity of the other ball.

Note: The other ball was at rest, therefore u₂ = 0 m/s

m₁u₁ = m₁v₁ + m₂v₂

making m₂ the subject of the equation above,

m₂ = (m₁u₁-m₁v₁)/v₂...................... Equation 1

Given: m₁ = 45 g, u₁ = 273 km/h, v₁ = -91 km/h(moves to the left), v₂ = 182 km/h

Substituting these values into equation 1

m₂ = [45×273 - 45(-91)]/182

m₂ = (12285 + 4095)/182

m₂ = 16380/182

m₂ = 90 g.

Thus the mass of the other ball = 90 g