Question

1. Two students are kayaking on the Saint John River. Initially, they are floating directly beside each other chatting and moving with the river current at 1.50 m/s downstream. Student A pushes away from Student B and sees Student B floating away from them at 1.00 m/s in the upstream direction. The combined inertia of Student A and their kayak is 100 kg and the combined inertia of Student B and their kayak is 120 kg. Assume that there is no friction between the kayaks and the water. a. Relative to the river flow, determine the velocities of the two students once they start moving away from each other (after the push). (Define your system to justify any conservation relations you might use, provide appropriate diagrams to describe the interaction and explain your solution approach.) b. What are the velocities of the two students once they are moving away from each other as seen from the perspective of someone on the shore of the river? c. What source energy does Student A expend in pushing the two kayaks apart?

Answer 1

let downstream direction be positive and upstream direction be negative.

initial velocity of each student :

student A , v1=1.5 m/s

student B, v2=1.5 m/s

after the push,

let velocity of student A is va and student B is vb.

as seen by student A, student B is moving at 1 m/s in upstream direction.

hence relative speed of B w.r.t. A =-1 m/s (negative sign due to upstream direction)

==>vb-va=-1…(1)

using conservation of momentum principle:

mass of student A*initial speed of A+mass of B*initial speed of B=mass of A*final speed of A+mass of B*final speed of B

==>100*1.5+120*1.5=100*va+120*vb

==>100*va+120*vb=330…(2)

solving equation 1 and 2 together,

va=2.0455 m/s

vb=1.0455 m/s

hence answers are :

part a:

velocity of A w.r.t. river flow=va-current speed=2.0455-1.5=0.5455 m/s

velocity of B w.r.t. river flow=vb-current speed=-0.4545 m/s(in upstream direction)

part b:

from the perspective of someone on the shore,

speed of A =2.0455 m/s

speed of B=1.0455 m/s

part c:

student A expends his kinetic energy due to speed along the current in pushing the two kayaks apart.