Solving Joe's Tricky Boat Problem: Find Boat Speed Relative to Joe

[NasuSama]

Homework Statement

Joe, standing stationary on a beach, sees a small boat of mass M = 179 kg go by at constant speed V = 25.2 m/s. Tom, a man of mass m = 91.8 kg, stands at rest at the back of the boat. Suddenly Tom begins to run toward the front of the boat at speed vrel = 2.93 m/s relative to the boat. Find the speed of the boat v, relative to Joe, while Tom is running.

Homework Equations

O.K.

p = mv

The Attempt at a Solution

MV = MV_F + m(V - V_rel) [I thought that Tom is traveling at V - V_rel velocity]
MV - m(V - V_rel) = MV_F
V_F = MV - m(V - V_rel)/M

...But wrong answer.

 

[NasuSama]

Any help?

 

[gneill]

Start by considering the boat and Tom in isolation. In other words, suppose that the boat and Tom are initially stationary in some frame of reference. Since no external forces act on this isolated system, the center of mass must remain stationary (conservation of momentum).

When Tom begins to run, the center of mass must continue to remain stationary. If that's so, what does that tell you about the sum of the momenta of Tom and the boat in this frame of reference?

 

[NasuSama]

Start by considering the boat and Tom in isolation. In other words, suppose that the boat and Tom are initially stationary in some frame of reference. Since no external forces act on this isolated system, the center of mass must remain stationary (conservation of momentum).

When Tom begins to run, the center of mass must continue to remain stationary. If that's so, what does that tell you about the sum of the momenta of Tom and the boat in this frame of reference?

I believe that the first time before Tom runs, it's just that m_b * v_b = p_initial [which is the boat's momentum]

Then, I guess that for the second part, we have...

m_b * v_bf + m_t * v_tf

 

[gneill]

I believe that the first time before Tom runs, it's just that m_b * v_b = p_initial [which is the boat's momentum]

Then, I guess that for the second part, we have...

m_b * v_bf + m_t * v_tf

Considering the boat and Tom in isolation, before Tom runs all velocities are zero.

This is a frame of reference specifically chosen such that the boat and Tom are initially at rest. Their motion with respect to the observer on the shore will be considered afterwards. The idea is to separate the effects caused by Tom's interaction with the boat and deal with that first, and then later place those effects into the shore-based observer's frame of reference.