You are on a skateboard of mass 5.00kg with a ball in hands (mass of the ball is 600kg). You throw the ball forward horizontally and find that you recoil back with 2.0m/s. What is the forward speed of the ball? (Use your own mass where needed).

Assume there is no friction and use conservation of total momentum.

M1 = skateboard mass
M2 = your mass
M3 = ball's mass
Vr = recoil velocity
Vb = ball velocity
(M1 + M2) Vr + M3 Vb = 0
Vr = -[M3/(M1 + M2)]*Vb
Plug in your numbers. Vr is negative because the recoil is in the opposite direction

To find the forward speed of the ball, we can apply the principle of conservation of momentum. According to this principle, the total momentum before throwing the ball should be equal to the total momentum after throwing the ball.

The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum before throwing the ball can be calculated by adding the momenta of the skateboard and the ball.

Let's assume the forward speed of the ball after being thrown is "v" m/s. As we're also given that the skateboard recoils back with a velocity of 2.0 m/s, we can calculate its velocity as well.

To apply the conservation of momentum, we need to calculate the momenta before and after throwing the ball.

Before throwing the ball:
Momentum of skateboard = mass of skateboard × velocity of skateboard = (5.00 kg) × (0 m/s) = 0 kg⋅m/s
Momentum of ball = mass of ball × velocity of ball = (600 kg) × (0 m/s) = 0 kg⋅m/s

Total momentum before = Momentum of skateboard + Momentum of ball = 0 kg⋅m/s + 0 kg⋅m/s = 0 kg⋅m/s

After throwing the ball:
Momentum of skateboard = mass of skateboard × velocity of skateboard = (5.00 kg) × (-2.0 m/s) = -10.00 kg⋅m/s (negative due to the opposite direction)
Momentum of ball = mass of ball × velocity of ball = (600 kg) × (v m/s)

Total momentum after = Momentum of skateboard + Momentum of ball = -10.00 kg⋅m/s + (600 kg) × (v m/s)

According to the conservation of momentum, the total momentum before throwing the ball is equal to the total momentum after throwing the ball. Therefore:

0 kg⋅m/s = -10.00 kg⋅m/s + (600 kg) × (v m/s)

Simplifying the equation:

10.00 kg⋅m/s = 600 kg × v m/s

Dividing both sides by 600 kg:

10.00 kg⋅m/s ÷ 600 kg = v m/s

v ≈ 0.017 m/s

Therefore, the forward speed of the ball after being thrown is approximately 0.017 m/s.