Starting from rest, a 1.6x10-4 kg flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of 0.38 N on it. This force does 2.6x10-4 J of work on the flea. (a) What is the flea's speed when it leaves the ground? (b) How far upward does the flea move while it is pushing off? Ignore both air resistance and the flea's weight.

To solve this problem, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the flea is equal to the change in its kinetic energy when it leaves the ground.

Let's go step by step:

(a) To find the flea's speed when it leaves the ground, we can use the equation:

Work done = change in kinetic energy

Given:
Work done = 2.6x10^-4 J

We know that the work done is also equal to the force applied multiplied by the distance over which the force is applied:

Work done = force * distance

Given:
Force = 0.38 N

Since the ground force is in the same direction as the displacement (upward), we can calculate the distance by dividing the work done by the force:

Distance = Work done / Force
Distance = 2.6x10^-4 J / 0.38 N

Now that we know the distance, we can solve for the final speed of the flea using the formula:

vf = sqrt(2ad + vi^2)

Since the flea starts from rest, the initial velocity (vi) is 0 m/s. Also, we can assume that the acceleration (a) is constant during the flea's upward motion and is given by:

a = force / mass

Given:
mass = 1.6x10^-4 kg

Now we have all the values needed to solve for the final speed (vf).

(b) To find how far upward the flea moves while pushing off, we can use the same equation for distance:

Distance = Work done / Force

Now we can substitute the values into the equation and solve for distance.

I hope this explanation helps you understand how to approach and solve the problem!