# A 28.0 kg crate is initially moving with a velocity that has magnitude 3.67 m/s in a direction 37.0 degrees west of north. How much work must be done on the crate to change its velocity to 6.25m/s...

A 28.0 kg crate is initially moving with a velocity that has magnitude 3.67 m/s in a direction 37.0 degrees west of north. How much work must be done on the crate to change its velocity to 6.25m/s in a direction 63.0 degrees south of east?

justaguide | College Teacher | (Level 2) Distinguished Educator

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A 28.0 kg crate is initially moving with a velocity that has magnitude 3.67 m/s in a direction 37.0 degrees west of north.

The components of the velocity of the crate is 3.67*sin 37 towards the West and 3.67*cos 37 towards the North. This has to be changed to a velocity to 6.25 m/s in a direction 63.0 degrees south of east? The components of the changed velocity is 6.25*cos 63 towards the East and 6.25*sin 63 towards the South

The acceleration required to change the velocity is 3.67*sin 37 - 6.25*cos 63 towards the East and 3.67*cos 37 - 6.25*sin 63 towards the South.

The net acceleration has a magnitude of 2.711 m/s^2 in the direction tan^-1((3.67*cos 37 - 6.25*sin 63)/(3.67*sin 37 - 6.25*cos 63)) = 76.59 degrees South of East.

It is not possible to determine the work done as the distance over which the force has to act is not given. Only the force required can be determined.

The force required is equal to 75.908 N in the direction 76.59 degrees South of East.