# Please help with this math problem?!!!A rocket is traveling straight up from its launch pad. An observer 5.00 km from the launch pad notices that at one instant, she must tilt her telescope 45.0...

Please help with this math problem?!!!

A rocket is traveling straight up from its launch pad. An observer 5.00 km from the launch pad notices that at one instant, she must tilt her telescope 45.0 degrees upward to see the rocket. 10.0 seconds later, she must tilt her rocket upward 50.0 degrees to see the rocket. What was the average speed of the rocket?

Hint: For average speed, use this equation for average velocity:

where d2 and d1 are the final and starting distances (so d2 – d1 is the distance traveled) and t is the time it took to travel that distance.

Another Hint: To get the two distances, remember your old friends the trig ratios.

Use a problem-solving strategy to solve this one. Number your paper with the problem letter, and show all work there.

A. Analyze the problem: Read the problem carefully, and make sure you know what you re supposed to find. List the "knowns," translating them into math or into shorthand.

What are your known quantities? List them in mathematical notation, setting each equal to a variable.

B. Convert the units: Convert all the given (known) quantities into SI units. (There are some exceptions to this, but you'll be told in the problem.)

C. Sketch the situation: This doesn't always apply, but do it whenever you can. It doesn't matter if you're artistic or not. Just take the time to draw a diagram, label the values you're given, and essentially restate the problem.

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### 1 Answer

We know `theta_1=45^o` and `theta_2=50^o`

Distance to rocket launch = 5km=5000m

We can find the height `h_1 = 5000*sin(theta_1)`

The second height (after 10 seconds) is `h_2=5000*sin(theta_2)`

So the average speed is `v_(av)=(h_2-h_1)/(10s)=5000/10(sin(50^o)-sin(45^o))`

We get `v_(av)=294.688 m//s` . Since the measurements were given with three decimals of acuracy, our answer should be `v_(av)=295m//s`