Solve the problem.
-A ramp leading to the entrance of a building is inclined upward at an angle of $3 ^ { \circ }$. A suitcase is to be pulled up the ramp by a handle that makes an angle of $38 ^ { \circ }$ with the horizontal. How much force must be applied in the direction of the handle so that the component of the force parallel to the ramp is 50 lbs.?
A) 40.96 lbs
B) 59.05 lbs
C) 63.36 lbs
D) -51.83 lbs

Question

Quizplus · Accepted Answer

First, we need to find the component of the force parallel to the ramp, which is:

$$F_{\parallel} = F \cos \theta$$

where F is the force applied in the direction of the handle and θ is the angle between the handle and the horizontal.

We know that F_{\parallel} = 50 lbs, and θ = 38°. Therefore:

$$50 = F \cos 38 ^ { \circ }$$

Solving for F, we get:

$$F = \frac { 50 } { \cos 38 ^ { \circ } } \approx 63.36 \text{ lbs}$$

Therefore, the answer is C.

Solve the Problem 3∘3 ^ { \circ }3∘ a Suitcase Is to Be Pulled Up the Ramp

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