A 1.08 kg skateboard is coasting along the pavement at a speed of 5.30 m/s when a 1.05 kg cat drops from a tree vertically downward onto the skateboard. What is the speed of the skateboard-cat combination?
To find the speed of the skateboard-cat combination after the cat drops onto the skateboard, we can use the law of conservation of momentum. According to this law, the total momentum before the cat drops onto the skateboard is equal to the total momentum after the cat drops onto the skateboard.
The formula for momentum is:
Momentum = mass x velocity
Before the cat drops, the momentum of the skateboard is given by:
Momentum of skateboard before = mass of skateboard x velocity of skateboard
= 1.08 kg x 5.30 m/s
= 5.724 kg·m/s
The cat is initially at rest, so its momentum before it drops is zero.
After the cat drops onto the skateboard, the total momentum of the skateboard-cat combination is the sum of the momenta of the skateboard and the cat:
Momentum of skateboard-cat combination after = (mass of skateboard + mass of cat) x velocity of skateboard-cat combination
Let's assume the speed of the skateboard-cat combination after the collision is V.
Using the conservation of momentum, we can write:
Momentum of skateboard before = Momentum of skateboard-cat combination after
5.724 kg·m/s = (1.08 kg + 1.05 kg) x V
5.724 kg·m/s = 2.13 kg x V
Divide both sides by 2.13 kg to solve for V:
V = 5.724 kg·m/s / 2.13 kg
V ≈ 2.69 m/s
Therefore, the speed of the skateboard-cat combination after the cat drops onto the skateboard is approximately 2.69 m/s.