Help! I'm Stuck with a Darn Trig Problem!?

Question

Hey… We were given this problem in class and I am having a difficult time solving/ understanding the question. I tried finding the resultant vector and then proceeding from there but then I got all sorts of awkward answers….

Here’s what I tried to find the magnitude:
√((Magnitude)cos (angle) + (Magnitude2) cos(angle2 ) + (Magnitude)sin (angle) + (Magnitude2) sin(angle2 ))

I then used tan to find the angles but this I believe was incorrect. Could someone perhaps attempt the problem and explain/ show how to do it? Thanks a bunch for your help:)

Here’s the problem:
A bus weighing 6,075 pounds exerts a force of 5,385 pounds on a hill where it is parked. What angle does the hill make with the horizontal? What force must be exerted by the brakes to prevent the bus from rolling down the hill?

Answer 1

You do look confused. Your nomenclature doesn't help you any. Basically, if the bus was on a "horizontal hill", the bus force exerted on the hill would be the same as its weight. As the hill is "tilted", some of the weight it exerted in the on the plane of the hill, and some vertical to this plane into the hill, but the RESULTANT pointing in the vertical direction is still the weight of the bus. You should draw a little picture of the bus on an incline with an angle Ah with the horizontal. From vector analysis, the angle Ah can be found from Ah = Cos-1(5385/6075) where you look up the ratio in the cosine table and find the angle Ah at which it occurs. The brake force is sqrt (6075^2 - 5385^2)

Answer 2

push force