# 2 Simple mechanism geometry problems

It's obviously been a while since I've worked some of these problems, and I thought I got it, but then something is tripping me up on each of these:

1) Rocket is fired vertically and tracked by radar--obtain an expression that relates the altitude and the horizontal distance between it and the radar dish. Plot the altitude vs. theta over the range 0<theta<75deg. when d=1mile.

I know I basically just need to get something of the height(theta) variety, but just can't seem to get the vectors worked out correctly to show what I know is happening. Have to do it in vector notation first, then make the plot.

2) Quick return mechanism shown consists of an arm of radius r that rotates about C in the slot of a bar pinned at O. Write a vector equation for the geometry of this mechanism, and fromt it get 2 scalar equations that relate the angles phi, theta, and the length x. Solve these for x and phi as functions of theta.

Again, I think I understand what happens here, but am having trouble getting started and figuring out the vector setup and then solve them out.

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SO simple, yet I'm still SO confused...any pointers in the right direction?

I've done a couple of other mechanism problems with 2 arms going to a point, and start out by breaking it apart a bit, and defining er and el (if that makes sense), with i and j.

But the layout of these two is confusing me. I'll try and get some of what I keep attempting scanned and linked.

mezarashi
Homework Helper
The first question is a very simple geometry/trigonometry problem. It's designed to help you gain confidence in applying math to real world problems! Draw a simple right triangle. The hypotenuse is (r), the horizontal side is (d), and the vertical side is (h).

According to the rules of geometry (sin, cos, tan), what is the relationship between the sides (h) and (d). There will be a theta involved, where theta is the angle squeezed between the sides (r) and (d).

Armed with this equation, can you now plot the graph over the given range with d=1?

I know how easy it should be, which just shows how bad my trig knowledge is.

For the first one, should it be: tan(theta)=h/d and then h=d*tan(theta)?

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mezarashi
Homework Helper
Yes, looks like it ^^.
For the second question. You'll probably have to use the more complicated-looking sin and cosine rules.