Question

Tom is climbing a 3.0-m-long ladder that leans against a vertical wall, contacting the wall 2.1 m above the ground. His weight of 880 N is a vector pointing vertically downward. (Weight is measured in newtons, abbreviated N.)

A) What is the magnitude of the component of Tom's weight parallel to the ladder?

B) What is the magnitude of the component of Tom's weight perpendicular to the ladder?

Answer 1

To find the components of Tom's weight parallel and perpendicular to the ladder, use trigonometry to calculate the magnitudes using the given angle of inclination.

Step-by-step explanation:

In this scenario, we can use trigonometry to find the components of Tom's weight parallel and perpendicular to the ladder.

A) To find the magnitude of the component of Tom's weight parallel to the ladder, we can use the formula: W|| = W * sin(angle), where W is the weight and angle is the angle between the ladder and the ground. So, W|| = 880 N * sin(25°).

B) To find the magnitude of the component of Tom's weight perpendicular to the ladder, we can use the formula: W₁ = W * cos(angle). So, W₁ = 880 N * cos(25°).

Answer 2

A)
`616\ \rm N`

B)
`628.44\ \rm N`

Step-by-step explanation:

Given:

Length of the ladder
`=3\ \rm m`

weight of the Tom
`W=880\ \rm N`

The angle that ladder make with x axis is

`\sin \theta=(2.1)/(3)\\\theta=44.42^\circ`

Part A

magnitude of the component of the weight parallel to the ladder
`=W\sin 44.42^\circ\\=880* \sin 44.42^\circ\\=616\ \rm N`

Part B)

The magnitude of the component of Tom's weight perpendicular to the ladder

`=W\cos 44.42^\circ\\=880* \cos 44.42^\circ\\=628.44\ \rm N`