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

[oMovements]

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
a_d=V_fd-V_id/t
=2.25-0/0.5
a_d=4.5m/s^2 [W]

F_g=m_dg
833=m(9.8)
m_d=85kg

F_net=m_da_d
F_g+F_d=m_da_d
833+F_d=-450.5

F_b+F_d=0
F_b= -F_d
F_b= 450.5N

F_b=m_ba_b
450.5=(375)(a_b)
a_b=1.26m/s^2

a_b=V_fb-V_ib/t
1.26=V_f-0/0.50
V_f= 0.63m/s

Is this correct?

 

[D H]

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.

 

[oMovements]

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.

F_d=m_da_d
=(85)(4.5)
F_d=382.5 N

F_b= -382.5 N

F_b=m_b(-a_b)
-382.5=(375)(-a_b)
(a_b)= 1.02 m/s^2

a_b= Vf-Vi/t
1.02=Vf-0/0.50
V_fb= 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?

 

[D H]

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

 

[oMovements]

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?

 

[D H]

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.