A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has magnitude 43.0 N and direction 61.0∘ south of west.

How much work does Paul's force do during a displacement of the crate that is 12.0 m in the direction 22.0∘ east of north?

The amount of work done is -512.13 joules

The given parameters are:

The amount of work done (W) is calculated using:

Where is the measure of angle between the force and the direction of the crate.

So, we have:

Recall that:

So, we have:

Evaluate cos(173)

Evaluate the products

Hence, the amount of work done is -512.13 joules

Read more about work done at:

link

The work done by Paul's force during the displacement of the crate is -512.15 J.

The given parameters:

The work done by Paul's force during the displacement of the crate is calculated as follows;

where;

θ is the angle between the force and the displacement

θ = 61⁰ + 90⁰ + 22⁰

θ =  173⁰

Thus, the work done by Paul's force during the displacement of the crate is -512.15 J.

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diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

50 inches should be the resultant vector