Starting from rest, a 1.7x10-4 kg flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of 0.44 N on it. This force does 2.4x10-4 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.

Why did the flea go to the gym? To work on its jumps!

(a) To find the flea's speed when it leaves the ground, we can use the work-energy principle. The work done on the flea is equal to the change in its kinetic energy. We have the equation:

Work = Change in Kinetic Energy

0.44 N * distance = 2.4x10^-4 J

Solving for distance, we get:

distance = 2.4x10^-4 J / 0.44 N

Using distance = speed * time and time = 2 * (speed / acceleration), we can find the time it takes for the flea to push off from the ground. Since the flea starts from rest, the initial velocity is 0 m/s and the final velocity can be found using the equation:

Final Velocity = Initial Velocity + Acceleration * Time

Since the final velocity when leaving the ground is the speed of the flea, we can rearrange the equation to solve for speed:

Speed = (Final Velocity - Initial Velocity) / Time

Substituting the known values, we get:

Speed = (Speed - 0) / (2 * (speed / acceleration))

Simplifying, we find:

Speed = (Speed * acceleration) / (2 * speed)

Solving for speed, we get:

Speed = acceleration / 2

Given that acceleration = Force / mass, we can calculate acceleration as:

acceleration = 0.44 N / 1.7x10^-4 kg

Plugging in the values, we get:

acceleration = 0.44 N / 1.7x10^-4 kg

Substituting this into our previous equation for speed, we find:

Speed = (0.44 N / 1.7x10^-4 kg) / 2

Calculating this, the flea's speed when it leaves the ground is:

Speed = 0.44 N / (1.7x10^-4 kg * 2)

(b) To find the distance upward the flea moves while pushing off, we already know the work done on the flea (2.4x10^-4 J) and the force applied by the ground (0.44 N). Since work is equal to force times distance, we can rearrange the equation to solve for distance:

Distance = Work / Force

Plugging in the values, we find:

Distance = 2.4x10^-4 J / 0.44 N

Calculating this, we can determine how far upward the flea moves while pushing off.

Remember, though, as a clown bot, my calculations might need fact-checking before going any further!

To solve this problem, we can apply the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the ground on the flea is equal to the change in the flea's kinetic energy.

Let's break down the problem step by step.

(a) What is the flea's speed when it leaves the ground?

We know that the work done on the flea is 2.4x10^(-4) J. This work is done by the average upward force of 0.44 N exerted by the ground on the flea.

The work done by a force can be calculated using the formula: work = force x distance x cos(theta), where theta is the angle between the force and the displacement of the object.

In this case, since the force exerted by the ground is acting in the same direction as the displacement (upward), theta is 0 degrees, and the cosine of 0 degrees is 1. Therefore, we can simplify the formula to:

work = force x distance

Therefore, 2.4x10^(-4) J = 0.44 N x distance

Rearranging the equation to solve for distance:

distance = (2.4x10^(-4) J) / (0.44 N)

distance = 0.545 x 10^(-4) m

Now, we can find the initial kinetic energy of the flea.

The initial kinetic energy is given by the formula: kinetic energy = 0.5 x mass x velocity^2

Since the flea starts from rest, its initial kinetic energy is zero.

Therefore, the work done on the flea (2.4x10^(-4) J) is equal to the change in kinetic energy.

Change in kinetic energy = Final kinetic energy - Initial kinetic energy

Change in kinetic energy = Final kinetic energy - 0

Final kinetic energy = Change in kinetic energy

Final kinetic energy = 2.4x10^(-4) J

Now we can equate the final kinetic energy to the formula for kinetic energy and solve for the final velocity:

2.4x10^(-4) J = 0.5 x (1.7x10^(-4) kg) x velocity^2

Solving for velocity:

velocity^2 = (2.4x10^(-4) J) / (0.5 x (1.7x10^(-4) kg))

velocity^2 = 2.4 / 1.7 m^2/s^2

velocity = √(2.4 / 1.7) m/s

Now, we can enter this equation into a calculator or simplifying it further to find the final velocity of the flea.

(b) How far upward does the flea move while it is pushing off?

We already calculated the distance upward as 0.545x10^(-4) m.

Therefore, the flea moves a distance of 0.545x10^(-4) m while pushing off.

So, the answers to the questions are:

(a) The flea's speed when it leaves the ground is √(2.4 / 1.7) m/s.
(b) The flea moves a distance of 0.545x10^(-4) m while pushing off.