Final answer:
To calculate the initial velocity of the wood block during the swing, use the principle of conservation of momentum. For the initial velocity of the ball, use the equation m₁v₁ = (m₁ + m₂)v₃. Solve the equations to find the velocities.
Step-by-step explanation:
To calculate the initial velocity of the wood block during the swing, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. Let v₁ be the initial velocity of the ball when it is launched and v₂ be the initial velocity of the wood block. Since the ball passes through the wood block, the final velocity of the ball is equal to the velocity of the wood block, which is v₂. So, we have: m₁v₁ + m₂v₂ = m₁v₃ + m₂v₃, where m₁ = mass of the ball, m₂ = mass of the wood block, and v₃ = final velocity of the ball and wood block. Substituting the given values, we get: (0.03 kg)(v₁) + (0.5 kg)(v₂) = (0.03 kg + 0.5 kg)(15 m/s) Solving this equation will give you the initial velocity of the wood block during the swing. To find the initial velocity of the ball when it is launched, you can use the equation: m₁v₁ = (m₁ + m₂)v₃ Substituting the values, we have:
(0.03 kg)(v₁) = (0.03 kg + 0.5 kg)(15 m/s) Solving this equation will give you the initial velocity of the ball when it is launched.