23. ssm (a) Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 445 newtons and is directed due west. The other pushes with a force , which has a magnitude of 325 newtons and is directed due north. What are the magnitude and direction of the resultant force     applied to the crate? (b) Suppose that the second worker applies a force   instead of . What then are the magnitude and direction of the resultant force   applied to the crate? In both cases express the direction relative to due west.

 

We have the following vector relationship for part (a)

 

This looks like this

Since  and  are at right angles we can use Pythagorean Theorem and the magnitude and direction are found from

And

Plugging the values

 

 

 

 

So the magnitude and direction are

 

 

For part (b),     the situation looks like

Again,  and  are at right angles we can use Pythagorean Theorem and the magnitude and direction are found from

And

Plugging the values

 

 

 

 

So the magnitude and direction are

 

 

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This page last updated on January 11, 2020