A 68.0 kg ice skater moving to the right with a velocity of 2.55 m/s throws a 0.16 kg snowball to the right with a velocity of 27.5 m/s relative to the ground.
(a) What is the velocity of the ice skater after throwing the snowball? Disregard the friction between the skates and the ice.
(b) A second skater initially at rest with a mass of 60.50 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
a. Conservation of momentum, the initial momentum. However, it is unclear where the snowball came from...was the ice skate carrying snow initially?
I think so
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided there are no external forces acting on the system.
(a) To find the velocity of the ice skater after throwing the snowball, we can consider the system consisting of the ice skater and the snowball before and after the throw. Initially, the ice skater has a mass of 68.0 kg and a velocity of 2.55 m/s to the right, while the snowball has a mass of 0.16 kg and a velocity of 27.5 m/s to the right (relative to the ground).
Using the conservation of momentum, we can write the equation:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the ice skater = 68.0 kg
v1 = initial velocity of the ice skater = 2.55 m/s
m2 = mass of the snowball = 0.16 kg
v2 = initial velocity of the snowball = 27.5 m/s
vf = final velocity of the ice skater
Substituting the given values into the equation, we can solve for vf:
(68.0 kg * 2.55 m/s) + (0.16 kg * 27.5 m/s) = (68.0 kg + 0.16 kg) * vf
173.4 kg·m/s + 4.4 kg·m/s = 68.16 kg * vf
177.8 kg·m/s = 68.16 kg * vf
vf = 177.8 kg·m/s / 68.16 kg
vf = 2.61 m/s
Therefore, the velocity of the ice skater after throwing the snowball is 2.61 m/s to the right.
(b) To find the velocity of the second skater after catching the snowball in a perfectly inelastic collision, we can consider the system consisting of the second skater and the snowball before and after the catch. Initially, the second skater is at rest, and the snowball has a mass of 0.16 kg and a velocity of 27.5 m/s to the right (relative to the ground).
Using the conservation of momentum, we can write the equation:
(m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the second skater = 60.50 kg
m2 = mass of the snowball = 0.16 kg
v2 = initial velocity of the snowball = 27.5 m/s
vf = final velocity of the combined system
Substituting the given values into the equation, we can solve for vf:
(0.16 kg * 27.5 m/s) = (60.50 kg + 0.16 kg) * vf
4.4 kg·m/s = 60.66 kg * vf
vf = 4.4 kg·m/s / 60.66 kg
vf = 0.073 m/s
Therefore, the velocity of the second skater after catching the snowball in a perfectly inelastic collision is 0.073 m/s to the right.