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

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Homework Help Overview

The problem involves a diver weighing 833 N diving from a boat with a mass of 375 kg, leaving the boat with a velocity of 2.25 m/s. The discussion centers around determining the final velocity of the boat after the diver's departure, considering the implications of Newton's third law.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between the diver's weight and mass, the effects of gravitational force, and the implications of horizontal velocity. There are attempts to calculate the boat's final velocity using various force equations and acceleration values.

Discussion Status

Some participants have pointed out errors in calculations and assumptions, particularly regarding the treatment of gravitational force and the direction of velocity. There is ongoing clarification about the relevance of direction in vector quantities and the distinction between different forces acting on the diver and the boat.

Contextual Notes

There is uncertainty regarding the application of gravitational force in the context of the problem, especially if the direction of the diver's velocity is not specified. Participants are questioning how to approach the problem under different assumptions about direction.

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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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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.
 
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:
You went from 382.5 N to 385.5 N. That's a mistake you carried through to your final answer.
 
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?
 
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.