A 60.0 kg girl stands up on a stationary floating raft and decides to go into shore. She dives off the 180 kg floating raft with a velocity of 4.0 m/s [W]. Ignore the substantial friction real objects in water experience.
a) What is the momentum of the girl as she is diving?
b) What is the momentum of raft as the girl is diving?
c) What is the final speed of the raft just after the girl dives?
a) * Let [W] be +ive.
p=mv
=(60.0kg)(4.0m/s)
=240 kg/(m/s)
Correct?
b) a little confused about this one, is it p=mv, and then =(180kg)(4.0m/s)=720kg/(m/s). this doesn't make sense because the raft doesn't have a velocity of 4m/s. (and it does say the raft is stationary- is it possible that the momentum=0?)i was thinking about calculating impulse, but i don't have the information. please help with this one.
c) for this one, i'm going to use p=p' (initial momentum=final momentum), and then work it out to be mv1 + mv2 = mv1' + mv2' where 1 is the girl, and two is the raft.. sub in what i know, and solve for v2'. in this case, would i use v1= 240 kg/(m/s) from part a, (ifso, what would i put for v1'), or would i put 0 for V1, and 240 for v1'? Thennnn, i would have to deal with the raft which i hope i get figured out from part b !
Thanks in advance!
For the the first part you have it right. For the second part, the momentum equals zero because the momentum before she just is zero. After she jumps, the make the total momentum zero, the momentum of the raft and the momentum of the girl must be equal in size but opposite in direction.
For the third part is the same. 0= (Mass of girl)*(velocity of girl) + (Mass of raft)*(velocity of raft)
a) The momentum of the girl as she is diving can be calculated using the formula p = mv.
P = (60.0 kg)(4.0 m/s) = 240 kg*m/s.
So, the momentum of the girl is 240 kg*m/s.
b) Since the raft is stationary, it does not have any initial velocity. Therefore, its initial momentum is zero. Thus, the momentum of the raft as the girl is diving is zero.
c) To calculate the final velocity of the raft just after the girl dives, you can use the principle of conservation of momentum. According to this principle, the total momentum before the dive should be equal to the total momentum after the dive.
Initially, the momentum of the girl is 240 kg*m/s, and the momentum of the raft is zero. Let's assume the final velocity of the girl is v1' and the final velocity of the raft is v2'. Using the conservation of momentum, we have:
m1v1 + m2v2 = m1v1' + m2v2'
Substituting the known values:
(60.0 kg)(4.0 m/s) + (180 kg)(0 m/s) = (60.0 kg)(v1') + (180 kg)(v2')
240 kg*m/s = (60.0 kg)(v1') + (180 kg)(v2')
Since the boy jumps off the raft, the final velocity of the girl, v1', can be assumed to be zero:
240 kg*m/s = (60.0 kg)(0 m/s) + (180 kg)(v2')
Simplifying,
240 kg*m/s = 180 kg(v2')
Dividing both sides by 180 kg,
1.33 m/s = v2'
So, the final speed of the raft just after the girl dives is approximately 1.33 m/s.
Hope this helps, and be sure to keep your humor afloat!
a) Yes, you have correctly calculated the momentum of the girl as she is diving:
p = mv
= (60.0 kg)(4.0 m/s)
= 240 kg/(m/s)
So, the momentum of the girl as she is diving is 240 kg/(m/s).
b) Since the raft is stationary, its initial velocity is 0. Therefore, the momentum of the raft is indeed 0:
p = mv
= (180 kg)(0 m/s)
= 0 kg/(m/s)
So, the momentum of the raft as the girl is diving is 0 kg/(m/s).
c) To find the final speed of the raft just after the girl dives, you can use the conservation of momentum:
Initial momentum = Final momentum
The initial momentum is 0 kg/(m/s) (since the raft is stationary), and the final momentum will be the sum of the momenta of the girl and the raft. Let's consider the girl as object 1 and the raft as object 2.
Initial momentum = 0 = m1v1 + m2v2
Plugging in the known values:
0 = (60.0 kg)(4.0 m/s) + (180 kg)(v2)
Simplifying the equation:
0 = 240 kg/(m/s) + (180 kg)(v2)
Rearranging the equation to solve for v2:
v2 = -240 kg/(180 kg) = -1.33 m/s
Since velocity is a vector quantity, the negative sign indicates that the final velocity of the raft is in the opposite direction to the girl's velocity.
So, the final speed of the raft just after the girl dives is approximately 1.33 m/s in the opposite direction of the girl's velocity.
a) To find the momentum of the girl as she is diving, you can use the formula p = mv, where p is the momentum, m is the mass, and v is the velocity. The given mass of the girl is 60.0 kg, and her velocity is 4.0 m/s [W].
So, plugging in the values:
p = (60.0 kg)(4.0 m/s [W])
p = 240 kg/(m/s)
Therefore, the momentum of the girl as she is diving is 240 kg/(m/s).
b) Since the raft is stationary, its initial velocity is 0 m/s. Therefore, its initial momentum would be 0 kg/(m/s) as well. The momentum of the stationary raft doesn't change when the girl dives off with a velocity. So, you are correct in your assumption that the momentum of the raft is zero.
c) To find the final speed of the raft just after the girl dives, you can make use of the law of conservation of momentum. According to this law, the total momentum before the dive should be equal to the total momentum after the dive.
In this case, we can set up the equation as follows:
(mass of the girl)(initial velocity of the girl) = (mass of the girl)(final velocity of the girl) + (mass of the raft)(final velocity of the raft)
Since the final velocity of the girl is given as 4.0 m/s [W], we can rewrite the equation as:
(60.0 kg)(0 m/s) = (60.0 kg)(4.0 m/s [W]) + (180 kg)(final velocity of the raft)
Simplifying the equation:
0 = 240 kg/(m/s) + (180 kg)(final velocity of the raft)
To solve for the final velocity of the raft, subtract 240 kg/(m/s) from both sides and divide by 180 kg:
(final velocity of the raft) = -1.33 m/s [W]
Therefore, the final speed of the raft just after the girl dives is 1.33 m/s westward.