Ann, a 66.1 kg person throws a 0.0460 kg snowball forward with a ground speed of 31.7 m/s. Billy, with a mass of 60.5 kg, catches the snowball. Both people are on skates. Ann is initially moving forward with a speed of 2.29 m/s, and Billy is initially at rest. After the snowball is exchanged (a) What is Ann’s velocity? (b) What is Billy’s velocity? Disregard friction between the skates and the ice.
m1=66.1 kg, v1=2.29 m/s
m2=0.046 kg, v2= 31.7 m/s
m3=60.5 kg, v3=0
u1=? u3=?
The law of conservation of linear momentum
(m1+m2) •v1 =m1•u1 +m2•v2
u1= [(m1+m2) •v1- m2•v2]/m1 =
=[(66.1+0.046) •2.29 – 0.046•31.7]/66.1 = 2.269 m/s
m2•v2=(m2+m3) •u3
u3= m2•v2/(m2+m3) =
=0.046•31.7/(0.046+60.5)=0.024 m/s
I got the correct answer for the thrower, but for the catcher to find the second velocity, I follow the formula but it still counts it as wrong. What could I be doing wrong?
To answer this question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the exchange of the snowball should be equal to the total momentum after the exchange.
Momentum is calculated as the mass multiplied by the velocity. Thus, we can use the equation:
Total initial momentum = Total final momentum
Let's start by calculating the total initial momentum. We need to find the individual momenta of Ann and the snowball.
The momentum of Ann is given by:
Momentum of Ann = mass of Ann x velocity of Ann
Mass of Ann = 66.1 kg
Velocity of Ann = 2.29 m/s
Momentum of Ann = 66.1 kg x 2.29 m/s
Now let's find the momentum of the snowball. The mass of the snowball is given as 0.0460 kg and its velocity is given as 31.7 m/s.
Momentum of the snowball = mass of the snowball x velocity of the snowball
Momentum of the snowball = 0.0460 kg x 31.7 m/s
Now we can calculate the total initial momentum by adding the momentum of Ann and the snowball.
Total initial momentum = Momentum of Ann + Momentum of the snowball
Next, let's calculate the total final momentum. After the exchange of the snowball, Ann's velocity will change, and Billy's velocity will also change.
(a) To find Ann's velocity after the exchange, we can use the equation:
Final momentum of Ann = mass of Ann x velocity of Ann (after exchange)
(b) To find Billy's velocity after the exchange, we can use the equation:
Final momentum of Billy = mass of Billy x velocity of Billy (after exchange)
Since it's mentioned that Billy is initially at rest, the final momentum of Billy is zero.
Now, we can set up the equation:
Total initial momentum = Final momentum of Ann + Final momentum of Billy
Again, recalling the conservation of momentum principle, the total initial momentum should be equal to the total final momentum:
Total initial momentum = Total final momentum
Substituting the values into the equation, we can solve for the velocities of Ann and Billy.
Please provide the values for mass of Billy and the mass of the snowball to continue the calculation.