Question

Two friends are sitting in a stationary canoe. At T=3.0 S the person at the front tosses a sack to the person in the rear, who catches the sac .2 s later. Which plot in figure Q 9.22 shows the velocity of the boat as a function of time? Positive velocity is forward, negative velocity is backward. Neglect any drag force on the canoe from the water.

Answer 1

The correct plot in Figure Q 9.22 showing the velocity of the boat as a function of time is Plot C. The toss and subsequent catch of the sack result in a change in momentum within the system, causing the boat's velocity to alter, as depicted in Plot C.

Step-by-step explanation:

When the person at the front of the canoe tosses the sack to the rear, it initiates an internal force within the system, altering the momentum. As per the conservation of momentum principle, the initial momentum before the toss should be equal to the final momentum after the toss. Initially, the canoe and the occupants possess zero external momentum.

However, when the sack is thrown, it imparts momentum to the rearward direction. As the sack is caught by the person at the rear, an equal but opposite momentum is applied to counteract the sack's momentum, leading to a change in the canoe's velocity. This change in momentum over time is represented by Plot C, showcasing an abrupt alteration in velocity during the sack's toss and catch event.

Mathematically, the momentum change can be explained as follows:
`\( \Delta p = m \cdot \Delta v \)`, where
`\( \Delta p \)` is the change in momentum, m is the mass of the sack, and
`\( \Delta v \)` is the change in velocity. As there are no external forces acting on the system apart from the sack toss, the initial and final momenta of the system before and after the toss respectively remain constant, resulting in the depicted change in velocity shown in Plot C. This abrupt change in momentum is indicative of the observed events' effects on the canoe's velocity graph, aligning with the principles of momentum conservation.

Here is complete question;

"Two friends are sitting in a stationary canoe. At t = 3.0 seconds, the person at the front tosses a sack to the person in the rear, who catches the sack 0.2 seconds later. Which plot in Figure Q 9.22 shows the velocity of the boat as a function of time? Positive velocity is forward, negative velocity is backward. Neglect any drag force on the canoe from the water. Consider the implications of the sack toss on the overall motion of the canoe, taking into account the conservation of momentum. Explain your choice based on the observed events and their effects on the canoe's velocity graph."