Question

A rope is tied to a tree 4.5 feet from the ground and then run through a pulley hooked to a vehicle 33 feet from the tree. If a person stands at the tree and pulls ten feet of the rope (after all slack is taken up) how far will the vehicle move?

Answer 1

Answer:

The vehicle displacement is 9.90 feet.

Explanation:

Given that,

Height of tree = 4.5 feet

Distance = 33 feet

According to figure,

We need to calculate the value of l

Using Pythagorean theorem

$l=\sqrt{(33)^2+(4.5)^2}$

We need to calculate the vehicle displacement

Using horizontal component

Vehicle displacement =horizontal component of pulled rope

$Vehicle\ displacement= d\cos\theta$

Where, $\theta$ is angle between rope and ground

d = pulled length of rope

$Vehicle\ displacement=10\times\dfrac{33}{\sqrt{(33)^2+(4.5)^2}}$

$Vehicle\ displacement=9.90\ feet$

Hence, The vehicle displacement is 9.90 feet.