How to solve for Jane (mass 40 kg),standing on slippery ice, catches her leaping dog (mass 15 kg) moving horizontally at 3 m/s. What is the speed of Jane and her dog after the catch?
9 m
1.3
To solve this problem, you can use the principle of conservation of momentum. The formula to calculate momentum is:
Momentum (p) = mass (m) * velocity (v)
According to the law of conservation of momentum, the total momentum before the catch is equal to the total momentum after the catch.
Let's calculate the initial momentum:
Initial momentum of Jane = mass of Jane * velocity of Jane = 40 kg * 0 m/s = 0 kg·m/s
Initial momentum of the dog = mass of the dog * velocity of the dog = 15 kg * 3 m/s = 45 kg·m/s
Since Jane is standing on a slippery ice with no initial velocity, her initial momentum is zero.
Now, let's calculate the total final momentum:
Final momentum = (mass of Jane + mass of the dog) * velocity of Jane and the dog
Final momentum = (40 kg + 15 kg) * velocity of Jane and the dog
To find the velocity of Jane and the dog after the catch, we need to know the value of the final momentum. Since the momentum is conserved, the value of the total final momentum is equal to the initial momentum, which is 0 kg·m/s.
0 kg·m/s = (40 kg + 15 kg) * velocity of Jane and the dog
Solving for the velocity of Jane and the dog:
0 = 55 kg * velocity of Jane and the dog
velocity of Jane and the dog = 0 m/s
Therefore, the speed of Jane and her dog after the catch is 0 m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the catch is equal to the total momentum after the catch.
The momentum of an object is given by the product of its mass and velocity (p = m*v).
Let's assume that Jane and her dog move together at a common velocity (v') after the catch.
Before the catch:
Jane's momentum (p₁) = mass of Jane * velocity of Jane (m₁ * v₁)
Dog's momentum (p₂) = mass of the dog * velocity of the dog (m₂ * v₂)
After the catch:
The combined momentum of Jane and her dog (p') = (mass of Jane + mass of the dog) * velocity (m₁ + m₂) * v'
Since momentum is conserved, we have p₁ + p₂ = p'.
Now, let's substitute the given values into the equation:
Jane (mass 40 kg), velocity = 0 m/s (since she is standing)
Dog (mass 15 kg), velocity = 3 m/s
Before the catch:
Jane's momentum (p₁) = 40 kg * 0 m/s = 0 kg⋅m/s
Dog's momentum (p₂) = 15 kg * 3 m/s = 45 kg⋅m/s
After the catch:
The combined momentum of Jane and her dog (p') = (40 kg + 15 kg) * v'
Since momentum is conserved, we can set p₁ + p₂ = p':
0 kg⋅m/s + 45 kg⋅m/s = (40 kg + 15 kg) * v'
45 kg⋅m/s = 55 kg * v'
To find the velocity (v'), we divide both sides by the total mass (55 kg):
v' = 45 kg⋅m/s ÷ 55 kg
v' ≈ 0.82 m/s
Therefore, the speed of Jane and her dog after the catch is approximately 0.82 m/s.