Kinetic Energy in Racing Question

[cd80187]

All right, here is the question

A father racing his son has 1/3 the kinetic energy of the son, who has 1/3 the mass of the father. The father speeds up by 1.6 m/s and then has the same kinetic energy as the son.

So to being with, I set up two equations equal to each other, since the only unknown is initial velocity. I set it up as

(2/3)(1/2)(3m)(1.6)squared = (1/2)(3m)(v initial +1.6) squared

So to sum this up, I used 3m to represent the fathers weight in reference to the kid. The KE of the first half is multiplied times 2/3 because the increase of 1.6 m/s equalized the KE of the father and the boy, therefore the 1.6 m/s accounted for the other 2/3 of the energy. And on the other side, the v initial plus 1.6 m/s represented the final velocity that equaled the sons KE. I then canceled out the 3m and the 1/2 and graphed the quadratic equation, but I am getting an answer of .359 m/s, and that is not right. How can i fix this, and am I even starting off correctly?

 

[berkeman]

The increase of 1.6m/s by the father triples his KE, which makes his KE equal to his son's KE. The equation you wrote does not quite express this. Besides, you may not need to involve the son at first. Can you get the father's Vi just from knowing that Vi + 1.6m/s triples his KE compared to just running at Vi? And then you can use masses and KEs to figure out the boy's Vi.

 

[kyle8921]

I would approach this problem by first confirming that the equations used are correct and that all variables are properly defined. I would also check for any errors in the calculations.

In this case, it seems that the equation used to represent the kinetic energy is correct, as it follows the formula KE = 1/2mv^2. However, the equation used to represent the father's initial kinetic energy is not accurate. It should be (1/3)(1/2)(3m)(v initial)^2, as the father has only 1/3 of the son's mass.

Additionally, it is important to note that the father's final kinetic energy is not equal to the son's initial kinetic energy. The father's final kinetic energy would be (1/2)(3m)(v initial + 1.6)^2, as you have correctly stated.

By making these corrections, the equation would be:

(1/3)(1/2)(3m)(v initial)^2 = (1/2)(3m)(v initial + 1.6)^2

From here, the quadratic equation can be solved to find the initial velocity of the father. It is also important to note that the final answer should be in units of meters per second, not just a decimal number.

Overall, it seems that the approach used is correct, but there were errors in the equations and calculations. Double-checking the equations and variables can help to avoid these errors and ensure an accurate solution.