Solve Third Law Problem: 833N Diver from 375kg Boat w/ 2.25m/s Velocity

In summary: No, that's not correct. You should ignore gravitational force here. Assume the diver leaves the boat with a horizontal velocity of 2.25 m/s. The only thing for which you need gravitational acceleration is the relationship between weight and mass.
  • #1
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Homework Statement
A diver with a weight of 833 N dives from a boat with a mass of 375kg. If he leaves the boat with a velocity of 2.25m/s [W] after accelerating for 0.50s, what will be the final velocity of the boat?

The attempt at a solution
ad=Vfd-Vid/t
=2.25-0/0.5
ad=4.5m/s^2 [W]

Fg=mdg
833=m(9.8)
md=85kg

Fnet=mdad
Fg+Fd=mdad
833+Fd=-450.5

Fb+Fd=0
Fb= -Fd
Fb= 450.5N

Fb=mbab
450.5=(375)(ab)
ab=1.26m/s^2

ab=Vfb-Vib/t
1.26=Vf-0/0.50
Vf= 0.63m/s

Is this correct?
 
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  • #2
No, that's not correct. You should ignore gravitational force here. Assume the diver leaves the boat with a horizontal velocity of 2.25 m/s. The only thing for which you need gravitational acceleration is the relationship between weight and mass.
 
  • #3
D H said:
No, that's not correct. You should ignore gravitational force here. Assume the diver leaves the boat with a horizontal velocity of 2.25 m/s. The only thing for which you need gravitational acceleration is the relationship between weight and mass.

Fd=mdad
=(85)(4.5)
Fd=382.5 N

Fb= -382.5 N

Fb=mb(-ab)
-382.5=(375)(-ab)
(ab)= 1.02 m/s^2

ab= Vf-Vi/t
1.02=Vf-0/0.50
Vfb= 0.51m/s

So I would do this then?

Also, if the direction of the velocity was not given to be [W] then would I use the gravitational force?
 
Last edited:
  • #4
You went from 382.5 N to 385.5 N. That's a mistake you carried through to your final answer.
 
  • #5
D H said:
You went from 382.5 N to 385.5 N. That's a mistake you carried through to your final answer.

Thanks, fixed my solution. But if the diver was not traveling horizontally and the direction west was not stated. Then would gravitational force apply?
 
  • #6
You have to know the direction. Velocity, acceleration, and force are vectors. Moreover, this is a 3rd law problem. The diver's interaction with the boat and with the Earth are two different interactions. You shouldn't mix them up.
 

1. How do you calculate the acceleration of the boat and diver?

The acceleration of the boat and diver can be calculated using Newton's Second Law, which states that force is equal to mass times acceleration. In this problem, we can use the given force of 833N and the combined mass of the boat and diver (375kg) to find the acceleration using the formula a = F/m. This gives us an acceleration of approximately 2.22 m/s^2.

2. What is the relationship between the force of the diver pushing off the boat and the force of the boat pushing back on the diver?

According to Newton's Third Law, for every action, there is an equal and opposite reaction. In this case, the force of the diver pushing off the boat (833N) is equal and opposite to the force of the boat pushing back on the diver (833N). This principle explains the motion of the boat and diver in opposite directions.

3. How do you find the velocity of the boat and diver after the diver jumps?

To find the velocity of the boat and diver after the jump, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity (which is 2.25m/s in this case), a is the acceleration, and t is the time. We know the acceleration from the first question and the time can be calculated by dividing the distance (2.25m) by the initial velocity. This gives us a final velocity of approximately 4.47m/s.

4. Is the mass of the diver important in this problem?

Yes, the mass of the diver is important in this problem as it affects the acceleration of the boat and diver. The greater the mass of the diver, the lower the acceleration will be. However, the mass of the diver does not affect the velocity after the jump, as seen in the previous question.

5. What other factors might affect the motion of the boat and diver in this problem?

Other factors that may affect the motion of the boat and diver in this problem include air resistance and friction between the boat and water. However, these factors are not mentioned in the problem and are assumed to be negligible. The shape and design of the boat may also affect the motion, but this is not specified in the problem either.

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