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

Answer:

$x = 12.027N$ and $y = 8.964N$

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.

$Sin\theta = \frac{y}{Force}$ ---- y component

$Cos\theta = \frac{x}{Force}$ ---- x component

Calculating the y component.

Substitute 15 for Force and 36.7 for $\theta$

$Sin\theta = \frac{y}{Force}$ becomes

$Sin(36.7) = \frac{y}{15}$

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 $\theta$

$Cos\theta = \frac{x}{Force}$ becomes

$Cos(36.7) = \frac{x}{15}$

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.