How Do You Calculate the Speed and Retarding Force in a Momentum Problem?

[TheRedDevil18]

Homework Statement

A boy of mass 60kg, running at 5m/s jumps on a stationary 15kg canoe and they move of together.

1.1) Find their speed just after the boy lands on the canoe
1.2) If the canoe comes to rest after moving through a distance of 15m, calculate the average magnitude of the retarding force on the canoe due to the water

Homework Equations

momentum before= momentum after
Impulse = Change in momentum

The Attempt at a Solution

Unsure about 1.2

1.1) 4m/s(momentum before = momentum after)
1.2) t=d/s = 15/4 = 3.75's

f*t = m*v
3.75f = 75(combined mass)*4
F = 80N

Could someone check

 

[sankalpmittal]

Hello TheRedDevil18,

Homework Statement

A boy of mass 60kg, running at 5m/s jumps on a stationary 15kg canoe and they move of together.

1.1) Find their speed just after the boy lands on the canoe
1.2) If the canoe comes to rest after moving through a distance of 15m, calculate the average magnitude of the retarding force on the canoe due to the water

Homework Equations

momentum before= momentum after
Impulse = Change in momentum

The Attempt at a Solution

Unsure about 1.2

1.1) 4m/s(momentum before = momentum after)

Correct !

1.2) t=d/s = 15/4 = 3.75's

f*t = m*v
3.75f = 75(combined mass)*4
F = 80N

Could someone check

Hmmm. Wrong. Constant resistive force is acting on the canoe system. You will have to use third equation of motion, v²=u²-2ad... Find deceleration a...

 

[TheRedDevil18]

Hello TheRedDevil18,



Correct !



Hmmm. Wrong. Constant resistive force is acting on the canoe system. You will have to use third equation of motion, v²=u²-2ad... Find deceleration a...

v^2 = u^2+2ad
16+30a = 0
a = -0.53m/s^-2

Fnet = ma
= 75*-0.53
= -39.75N

Would this be correct?

 

[sankalpmittal]

v^2 = u^2+2ad
16+30a = 0
a = -0.53m/s^-2

Fnet = ma
= 75*-0.53
= -39.75N

Would this be correct?

It is asking for the average retarding force exerted on the canoe system, and not the "canoe+boy" system.

You need to consider the mass of canoe only.

 

[Nickie]

this over and provide feedback?

Your solution for 1.1 is correct. For 1.2, you have correctly used the equation for impulse, but there are a few things to consider. First, the canoe is coming to rest, so its final velocity is 0. This means that the change in momentum is equal to the initial momentum (since the final momentum is 0). So, we can write the equation as:

Impulse = m*v - m*v0

Where m is the mass of the canoe, v is the final velocity, and v0 is the initial velocity (which we know is 5m/s). We can also use the equation for average force, which is:

Average force = Impulse / time

Substituting in our values, we have:

Average force = m*v - m*v0 / t

= (15kg)(0m/s) - (15kg)(5m/s) / 3.75s

= -75N / 3.75s

= -20N

Note that the negative sign indicates that the force is acting in the opposite direction of the motion, which makes sense since the canoe is slowing down. So, the average magnitude of the retarding force on the canoe due to the water is 20N.