A 68 student consumes 2500 Cal each day and stays the same weight. One day, he eats 3500 Cal and, wanting to keep from gaining weight, decides to "work off" the excess by jumping up and down. With each jump, he accelerates to a speed of 3.4 before leaving the ground.

Kinetic energy of jump = (1/2) m v^2

= (1/2)(68)(3.4)^2 = 393 Joules

.25(3500-2500) = 250 food calories to burn
1 food calorie (1000 physics heat calories) = 4184 Joules

250 Cal * 4184 J/Cal = 1,046,000 Joules

so
1,046,000/393 = 2661 Jumps

I was working on your final version.

Sorry, Damon. I thought she'd posted exactly the same question a dozen times, so I deleted the extras.

LOL - does not matter. I had already copied the last one.

To calculate the number of jumps the student needs to "work off" the excess calories, we can follow these steps:

Step 1: Calculate the extra calories consumed
The student consumed 3500 Cal in a day, which is 2500 Cal more than their usual intake. Therefore, the extra calories consumed are 2500 Cal.

Step 2: Calculate the amount of work needed to burn off the extra calories
To determine the work needed, we can use the equation:

Work = Force × Distance

In this case, the force is equal to the weight of the student, and the distance is the height reached during each jump.

Step 3: Calculate the weight of the student
To calculate the weight of the student, we can use the formula:

Weight = mass × acceleration due to gravity

Given that the student stays the same weight, we can assume that their weight is balanced by the normal force, which equals their weight.

Step 4: Calculate the height reached with each jump
To calculate the height reached during each jump, we can use the equation:

Final Velocity² = Initial Velocity² + 2 × acceleration × distance

Given that the final velocity is 0 m/s at the highest point of the jump (when the student leaves the ground), the equation simplifies to:

0 = (3.4 m/s)² + 2 × acceleration × distance

Since we're interested in the distance, we need to solve for it.

Step 5: Determine the number of jumps needed
Now that we know the height reached during each jump, we can calculate the number of jumps needed to burn off the extra calories. To do this, we divide the work needed to burn off the calories by the work done during each jump.

Finally, we can perform the necessary calculations to find the solution to the problem.