A man pulls a crate of mass 63.0 kg across a level floor. He pulls with a force of 174.0 N at an angle of 22.0° above the horizontal. When the crate is moving, the frictional force between the floor and the crate has a magnitude of 124.0 N.

If the crate starts from rest, how fast will it be moving after the man has pulled it a distance of 2.90 m?

Find the component of the man's force parallel to the floor. Subtact the force due to kinetic friction to get the net force. Use acceleration=force/mass to find the acceleration. For an initial velocity of 0, use v=sqrt(2*acceleration*distance) to calculate the speed at 2.90m

To find the speed at which the crate will be moving after being pulled a distance of 2.90 m, we can use 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 on the crate is the work done by the man pulling it, minus the work done by the frictional force. The net work done is equal to the change in kinetic energy of the crate.

So, let's calculate the work done by the man:

Work done by the man = force * distance * cos(theta)
= 174.0 N * 2.90 m * cos(22.0°)

Next, let's calculate the work done by the frictional force:

Work done by frictional force = Frictional force * distance
= 124.0 N * 2.90 m

The net work done is the difference between the work done by the man and the work done by the frictional force:

Net work done = Work done by the man - Work done by frictional force

Now, we can set the net work done equal to the change in kinetic energy of the crate, which is given by:

Change in kinetic energy = (1/2) * mass * velocity^2

Since the crate starts from rest, the initial kinetic energy is zero, and thus the change in kinetic energy is equal to the final kinetic energy.

Setting the net work done equal to the change in kinetic energy gives us:

Net work done = (1/2) * mass * velocity^2

Plugging in the values we have:

(Work done by the man - Work done by frictional force) = (1/2) * mass * velocity^2

Solving for velocity:

velocity^2 = [(Work done by the man - Work done by frictional force) * 2] / mass

Finally, taking the square root of both sides gives us the velocity of the crate:

velocity = √([(Work done by the man - Work done by frictional force) * 2] / mass)

So, substituting the values given:

velocity = √([(174.0 N * 2.90 m * cos(22.0°) - 124.0 N * 2.90 m) * 2] / 63.0 kg)

Evaluating this expression will give us the velocity of the crate.