Calculate Recoil Velocity: 4.85kg Stone & 102kg Canoe

  • Thread starter Jacque77
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In summary, the stone is thrown with a velocity of 7.73 m/s at an angle of 35.3 ° above the horizontal and the person and canoe have a combined mass of 102 kg. The recoil velocity is -0.28327 m/s.
  • #1
Jacque77
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Homework Statement



First: My course has sig figs disabled. We are recording all that is shown in calculations. Its my instructor's choice, not mine. Please do not lecture on sig figs. I know already. ;)
Problem:
A person stands in a stationary canoe and throws a 4.85-kg stone with a velocity of +7.73 m/s at an angle of 35.3 ° above the horizontal. The person and canoe have a combined mass of 102 kg. Ignore air resistance and effects of the water and find the horizontal recoil velocity (magnitude and direction) of the person and canoe.


The Attempt at a Solution



horizontal velocity = velocity of 7.73m/s * cos 35.3 = 6.3087
mass of stone 4.58kg * horizontal velocity of 6.3087 = 28.894 kg m/s
28.894 kg m/s = 102kg * recoil velocity
28.894 / 102 = recoil velocity = -0.28327 m/s This is incorrect. What have I done wrong? The negative is for the opposite direction movement.
 
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  • #2
Do you know the answer? Also, check the exact wording of the problem once more, in case something has been missed.
 
  • #3
Jacque77 said:

Homework Statement


A person stands in a stationary canoe and throws a 4.85-kg stone with a velocity of +7.73 m/s at an angle of 35.3 ° above the horizontal. The person and canoe have a combined mass of 102 kg. Ignore air resistance and effects of the water and find the horizontal recoil velocity (magnitude and direction) of the person and canoe.


The Attempt at a Solution



horizontal velocity = velocity of 7.73m/s * cos 35.3 = 6.3087
mass of stone 4.58kg * horizontal velocity of 6.3087 = 28.894 kg m/s
28.894 kg m/s = 102kg * recoil velocity
28.894 / 102 = recoil velocity = -0.28327 m/s This is incorrect. What have I done wrong? The negative is for the opposite direction movement.

Presumably, either 4.85 kg. or 4.58 kg. is correct for the mass of the stone. (I also want to stay away from someone who can throw an 11 pound stone that fast...). Somewhere you have a copying error, which may explain why the computer didn't like your answer...
 

1. How do you calculate the recoil velocity of a 4.85kg stone and a 102kg canoe?

The recoil velocity can be calculated using the principle of conservation of momentum. This states that the total momentum before and after a collision must be equal. So, in this case, we can use the equation p1 = p2, where p1 is the initial momentum of the stone and canoe and p2 is the final momentum after the collision.

2. What is the initial momentum of the stone and canoe?

The initial momentum can be calculated by multiplying the mass and velocity of each object. In this case, the initial momentum of the stone is 4.85kg multiplied by its initial velocity, which we will assume is 0m/s. The initial momentum of the canoe is 102kg multiplied by its initial velocity, which we will also assume is 0m/s.

3. What is the final momentum of the stone and canoe after the collision?

The final momentum can be calculated by adding the individual momentums of the stone and canoe after the collision. So, if the stone and canoe move in opposite directions after the collision, the final momentum would be the initial momentum of the stone minus the initial momentum of the canoe.

4. How do you calculate the final velocity of the stone and canoe?

Using the final momentum calculated in the previous question, the final velocity can be determined by dividing the final momentum by the combined mass of the stone and canoe. This will give you the final velocity of both the stone and canoe after the collision.

5. Can you provide an example calculation for the recoil velocity of a 4.85kg stone and a 102kg canoe?

Sure, let's say the stone has an initial velocity of 10m/s and the canoe has an initial velocity of -5m/s (moving in opposite directions). This means the initial momentum of the stone is 4.85kg x 10m/s = 48.5kgm/s and the initial momentum of the canoe is 102kg x (-5m/s) = -510kgm/s. After the collision, the final momentum would be 48.5kgm/s - (-510kgm/s) = 558.5kgm/s. Dividing this by the combined mass of 106.85kg, the final velocity would be 5.23m/s for both the stone and canoe.

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