A 66.5 kg ice skater moving to the right with
a velocity of 2.72 m/s throws a 0.104 kg snow-
ball to the right with a velocity of 40.3 m/s
relative to the ground.
What is the velocity of the ice skater after
throwing the snowball? Disregard the friction
between the skates and the ice.
Answer in units of m/s
Well, well, well, looks like the ice skater has decided to throw a snowball, huh? I hope they yell "Snowball!" while doing it, because that would be hilarious!
But let's get down to business. We need to find the velocity of the ice skater after throwing the snowball. We can use the principles of conservation of momentum here!
The momentum of an object is given by the formula:
momentum = mass × velocity
So, let's calculate the momentum of the ice skater before throwing the snowball:
momentum_before = (66.5 kg) × (2.72 m/s)
Now, let's calculate the momentum of the snowball:
momentum_snowball = (0.104 kg) × (40.3 m/s)
According to the law of conservation of momentum, the total momentum before throwing the snowball should be equal to the total momentum after throwing it. So, let's write that as an equation:
momentum_before = momentum_snowball + momentum_after
Now since the ice skater and the snowball are interacting, their momenta should be in opposite directions (according to Newton's third law). Hence, the momentum of the ice skater after throwing the snowball would be in the opposite direction as well.
Alright, let's solve the equation for momentum_after:
momentum_after = momentum_before - momentum_snowball
Substituting the values into the equation, we get:
momentum_after = (66.5 kg × 2.72 m/s) - (0.104 kg × 40.3 m/s)
And if we calculate that, we find that the velocity of the ice skater after throwing the snowball is approximately -1.69 m/s. Note the negative sign indicates the change in direction.
So, there you have it! The ice skater ends up moving to the left with a velocity of about 1.69 m/s after throwing the snowball. Keep practicing those snowball throws, my friend!
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before throwing the snowball should be equal to the total momentum after throwing the snowball.
The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of the ice skater as M and the mass of the snowball as m.
Before throwing the snowball:
The momentum of the ice skater is given by: Momentum of skater = Mass of skater * Velocity of skater
After throwing the snowball:
The momentum of the ice skater and snowball combined should be equal to the momentum of the skater before throwing the snowball.
Momentum of ice skater + Momentum of snowball = 0
Using the principle of conservation of momentum, we can write the equation:
Momentum of skater before throwing the snowball = Momentum of skater + Momentum of snowball
M * 2.72 m/s = (M + m) * V
Now we can solve for V, the velocity of the skater after throwing the snowball:
(M * 2.72 m/s) / (M + m) = V
Substituting the given values:
(66.5 kg * 2.72 m/s) / (66.5 kg + 0.104 kg) = V
Calculating this expression, we find:
(180.38 kg*m/s) / 66.604 kg = V
V ≈ 2.71 m/s
Therefore, the velocity of the ice skater after throwing the snowball is approximately 2.71 m/s.
To find the velocity of the ice skater after throwing the snowball, we can use the law of conservation of momentum.
The law of conservation of momentum states that the total momentum of a system remains constant when no external forces act on it. In this case, since there is no friction between the skates and the ice, we can consider the ice skater and the snowball as a closed system.
The momentum before throwing the snowball is equal to the momentum after throwing the snowball. Mathematically, this can be expressed as:
(mass of ice skater * initial velocity of ice skater) + (mass of snowball * initial velocity of snowball) = (mass of ice skater * final velocity of ice skater) + (mass of snowball * final velocity of snowball)
Plugging in the given values:
(66.5 kg * 2.72 m/s) + (0.104 kg * 40.3 m/s) = (66.5 kg * final velocity of ice skater) + (0.104 kg * 0 m/s)
Simplifying the equation:
180.68 kg*m/s + 4.1992 kg*m/s = 66.5 kg * final velocity of ice skater
184.8792 kg*m/s = 66.5 kg * final velocity of ice skater
Dividing both sides by 66.5 kg:
(final velocity of ice skater) = 184.8792 kg*m/s / 66.5 kg
(final velocity of ice skater) ≈ 2.78 m/s
Therefore, the velocity of the ice skater after throwing the snowball is approximately 2.78 m/s.