Question

A basketball and a golfball are heading toward each other, each with a speed of 2 m/s. The balls then collide head-on. If the basketball weighs 5 times as much as the golfball, and the collision can be considered elastic, what is the final speed of the golfball

Answer 1

The final speed of the golfball after colliding head-on with the basketball is 10 m/s.

Step-by-step explanation:

When two objects collide elastically, the total momentum and total kinetic energy of the system are conserved. In this case, the basketball and the golfball are moving towards each other with the same speed, so the initial total momentum of the system is zero. After the collision, the golfball will move in the opposite direction, but with the same speed as before since the collision is elastic.

Since the basketball weighs 5 times as much as the golfball, the final speed of the golfball will also be 5 times the initial speed of the basketball, which is 2 m/s. Therefore, the final speed of the golfball will be 10 m/s.

Answer 2

The final velocity of the golfball after an elastic collision with a basketball is 6 m/s. This is calculated using the principles of conservation of momentum and kinetic energy.

Step-by-step explanation:

To determine the final speed of the golfball after an elastic collision with a basketball, we can use the conservation of momentum and kinetic energy, because in an elastic collision, both quantities are conserved. Let's denote the mass of the golfball as m, the mass of the basketball as 5m (since it is given that the basketball weighs 5 times as much as the golfball), and the initial speed of both balls as v = 2 m/s.

Using the conservation of momentum, we have:

• m*(-v) + 5m*(v) = m*Vg + 5m*Vb
• -2m + 10m = m*Vg + 5m*Vb

Using the conservation of kinetic energy (since the collision is perfectly elastic), we get:

• ½*m*(v^2) + ½*5m*(v^2) = ½*m*(Vg^2) + ½*5m*(Vb^2)
• ½*(2^2) + ½*5*(2^2) = ½*(Vg^2) + ½*5*(Vb^2)
• 2 + 10 = ½*(Vg^2) + ½*5*(Vb^2)

Solving the simultaneous equations, the final velocity of the golfball (Vg) can be found to be 6 m/s. This is due to both balls exchanging their velocities due to the symmetric nature of the problem and the mass ratio.