Question

A dog pulls on a leash with a force of 15 23 is a big dog. The leash makes an angle of 36.7 degrees to the horizontal. What are the x

and y components of the force?

Answer 1

`x = 12.027N` and
`y = 8.964N`

Step-by-step explanation:

The first sentence of this question is not explanatory enough. However, I'll assume the force to be 15N

`Force = 15N`

`\theta = 36.7` to the horizontal

Required

Solve for the x and y components

Since the given angle is to the horizontal, the x and y coordinates are calculated using the following illustrations.

`Sin\theta = (y)/(Force)` ---- y component

`Cos\theta = (x)/(Force)` ---- x component

Calculating the y component.

Substitute 15 for Force and 36.7 for
`\theta`

`Sin\theta = (y)/(Force)` becomes

`Sin(36.7) = (y)/(15)`

Make y the subject

`y = 15 * Sin(36.7)`

`y = 15 * 0.5976`

`y = 8.964N`

Calculating the x component.

Substitute 15 for Force and 36.7 for
`\theta`

`Cos\theta = (x)/(Force)` becomes

`Cos(36.7) = (x)/(15)`

Make y the subject

`x = 15 * Cos(36.7)`

`x = 15 * 0.8018`

`x = 12.027N`

Hence, the x and y components of the force are: 8.964N and 12.027N respectively.