Question

In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. A rider is towed at a constant speed by a rope that is at an angle of 17° from horizontal. The tension in the rope is 1900 N. The force of the sail on the rider is 30∘ from horizontal. What is the weight of the rider?

Answer 1

Answer:

the weight of the rider is 493.53 N

Explanation:

Given the data in the question and as illustrated in the image below,

Tension T = 1900 N

the rider is moving at a constant speed so the net force in the horizontal direction will be 0

In the horizontal direction

F$_{sail$cos( 30° ) = Tcos ( 17° )

F$_{sail$ = Tcos( 17° ) / cos( 30° )

F$_{sail$ = 1900cos( 17° ) / cos( 30° )

F$_{sail$ = 2098.07 N

Now, In the vertical direction,

F$_{sail$ sin( 30° ) = W + T sin( 17° )

W = F$_{sail$ sin( 30° ) - T sin( 17° )

W = 2098.07sin( 30° ) - 1900sin( 17° )

W = 1049.035 - 555.506

W = 493.53 N

Therefore, the weight of the rider is 493.53 N