Two friends are sitting in a stationary canoe. At the person at the front tosses a sack to theperson in the rear, who catches the sack 2 later. Which plot in the figure shows thevelocity of the boat as a function of time? Positive velocity isforward, negative velocity is backward. Neglect any drag force onthe canoe from the water.
If the sack was heavier than in part A, how would the graph change? Assume the speed with which the heavier sack is thrown is the same as in part A.
We cannot see what the plots in your figure look like.
The boat will travel backwards between the time the sack is thrown and when it is caught. While the sack is in the air the boat will have a constant negative velocity. After it is caught its velocity will again be zero.
If the sack was heavier than in part A and the speed with which it is thrown remains the same, the graph of the velocity of the boat as a function of time would change as follows:
1. The initial velocity before the sack is thrown would remain the same.
2. When the sack is thrown, there would be a sudden decrease in velocity due to the impulse from the throw.
3. As the person in the rear catches the heavier sack, there would be a larger impulse acting on the boat, causing a more significant change in velocity.
4. Therefore, the downward slope of the graph during the time of catching the sack would be steeper compared to the lighter sack.
5. After the sack is caught, the velocity would gradually return to its original value as the two friends reach a new equilibrium in the stationary canoe.
In summary, the graph would show a steeper downward slope during the time of catching the sack, indicating a greater change in velocity due to the heavier weight of the sack.
To determine how the graph of velocity would change if the sack was heavier, we need to understand the principles of Newton's third law of motion and the concept of momentum.
Newton's third law of motion states that for every action, there is an equal and opposite reaction. In this case, when the person at the front of the canoe throws the sack towards the person in the rear, they exert a force on the sack, causing it to move in one direction. Simultaneously, according to Newton's third law, the sack exerts an equal and opposite force on the person throwing it, causing them to move in the opposite direction.
Now, let's consider the concept of momentum. Momentum is the product of an object's mass and its velocity. When the lighter sack is thrown from the front to the rear of the canoe, it carries a certain amount of momentum. According to Newton's third law, the person at the front also experiences an equal and opposite momentum, causing the canoe to move in the opposite direction.
Since momentum is conserved, if the sack is heavier, it will have more momentum when thrown from front to rear. Consequently, the person at the front and the canoe will experience a larger momentum in the opposite direction. Consequently, the graph of the canoe's velocity as a function of time will show a higher negative velocity (backward motion) in comparison to the graph for the lighter sack.
Therefore, if the sack is heavier, the graph of the canoe's velocity will show a more negative value (larger backward motion) during the time the sack is in the air, compared to the graph for the lighter sack.