Finding Initial Angle for a Projectile to Hit a Target 10,000 ft Away

[Marcin H]

Homework Statement

:
[/B]
Find two elevation angles that will enable a shell, fired from

ground level with a muzzle speed of 800 ft/s, to hit a groundlevel

target 10,000 ft away.

Homework Equations

Look at attached picture

The Attempt at a Solution

Look at attached picture

***I get to cos(x)sin(x)=1/4, but I don't think you can solve that for an angle x...

 

[Marcin H]

***UPDATE***

I got one of the angles, and it checks out with the answer key, but how on Earth do I get the angle of 15?

MY WORK:

ANSWER KEY:

 

[Mark44]

***UPDATE***

I got one of the angles, and it checks out with the answer key, but how on Earth do I get the angle of 15?

MY WORK:
View attachment 89769
ANSWER KEY:
View attachment 89770

You have a mistake in your work. As best as I can tell, your answer is close only due to a coincidence.

One of your equations is $50\sin(\theta) = t$ and the other is $800 \cos(\theta)t = 10000$
Your mistake is in solving for $\sin(\theta)$ in the first equation. It should be $\sin(\theta) = \frac t {50}$.

BTW, please make an effort to post your work here, rather than as an image. Your work is somewhat difficult to read.

 

[azizlwl]

S=ut-½at². (1)
R=vt. (2)

Just eliminate t, and substitute data in the last equation.