Mechanics/Projectiles/Angles/Trig. Identities?

[JamieB2]

Homework Statement

http://img213.imageshack.us/img213/1681/question1su9.png

Apologies for the scrappy diagram. My MS Paint skills aren't amazing.

Homework Equations

Personally, I'm not too sure. This question (I think) involves things that I haven't studied, I tried to do a little research into it on the Internet but it didn't help too much in the end. All I could really think of was

sec $$\theta$$ = 1/cos$$\theta$$

tan^2 $$\theta$$ + 1 = sec^2 $$\theta$$

sin^2 $$\theta$$ + cos^2 $$\theta$$ = 1

tan^2 $$\theta$$ = (1 - cos2$$\theta$$)/(1 + cos2$$\theta$$)

cos2$$\theta$$ = (2cos^2$$\theta$$ -1)

And maybe Pythagoras' theorem

The Attempt at a Solution

(Note; for ease of writing on paper, I replaced $$\alpha$$ with $$\theta$$, because, pathetic as it sounds, I don't like writing $$\alpha$$)

A bit of a mess, one of my lines of work went;

49sin^2$$\theta$$ + 49cos$$\theta$$ = 2401 = 49^2

sin^2 $$\theta$$ + cos^2 $$\theta$$ = 1

Divide all by cos^2$$\theta$$

(sin^2$$\theta$$)/(cos^2$$\theta$$) + 1 = sec^2$$\theta$$

tan^2$$\theta$$ + 1 = sec^2$$\theta$$

Which, obviously, doesn't help towards my answer.

What I'm most interested in is a kind of kick start, if I knew what kind of thing I'm supposed to do, I'd maybe be able to do the question myself, but I honestly do not know where to start.

 

[Doc Al]

This is meant as a physics problem, not a math problem. So start with the equations for projectile motion. Write expressions for the position as a function of time, treating vertical and horizontal position separately. Combine those equations to see what you can deduce about the launch angle.

 

[m2003]

I would recommend approaching this problem by first breaking it down into smaller parts and identifying what is given and what is being asked for. From the diagram, it appears that we are dealing with a projectile motion problem, where an object is launched at an angle \theta with a certain initial velocity. The goal is to find the maximum height reached by the object.

To solve this problem, we can use the equations of projectile motion, which involve trigonometric identities. These identities help us relate the different components of the motion, such as the initial velocity, angle, and time of flight. Some of the identities that may be useful in this problem are the ones listed in the homework section, such as the Pythagorean theorem and the trigonometric identities for secant, tangent, and cosine.

To start, we can use the given information to determine the initial velocity in terms of \theta using the trigonometric identity for cosine. Then, we can use the equations of projectile motion to determine the time of flight and the maximum height reached by the object. These equations involve the trigonometric identities for secant, tangent, and cosine, so it would be helpful to review these identities and understand how they are used in projectile motion problems.

Overall, the key to solving this problem is to identify what information is given and what is being asked for, and then using the appropriate equations and trigonometric identities to find the solution. It may also be helpful to draw a diagram and label all the components involved in the motion. I hope this helps to get you started on solving this problem. Good luck!