Angled Projectile at an elevated height

[darkdeeds]

Homework Statement

Many modern 3D video games must be designed such that objects move in ways as close as possible to reality. This is often called “game physics”, which is run by a physics engine coded into the game. In one event of a recent game, a player’s job is to shoot a cannon at objects on a distant cliff. The target is supposed to be at a distance of 400 m and is at a slight elevation with respect to the player – say 150 m – and the launch speed of the cannonball is supposed to be 100 m/s relative to the player's “stationary” avatar. The game physics ignores wind resistance (many if not all of them do). At what angles should the cannon be fired in order to hit the target?

Homework Equations

1/cos^2(x)=tan^2(x)+1
v=d/t
Vf=Vo+at
d=Vot+(1/2)at^2
d=(Vf^2+Vo^2)/2a
a=9.81 m/s^2

The Attempt at a Solution

I don't even know where to start, I'm aware that there are 2 angle with the difference being 90-x(angle).

 

[BruceW]

hi darkdeeds, welcome to physicsforums :) Is this part of homework? Anyway, I think your 5th equation is not quite right. It should be:
d=(Vf^2-Vo^2)/2a
And about the question itself, have you done these types of question before? What do you know about finding the components of velocity in vertical and horizontal directions? And what do you know about how the equations of motion work for vertical and horizontal motion?

 

[darkdeeds]

I've had similar questions to ones like this, however, I'm having difficulty finding the value for theta, and am not sure on how it is to be calculated without the time given. We've had questions like this before but they supplied more information.

 

[darkdeeds]

I was able to figure out the larger angle, which is 77.6 degrees, I am instructed to find the smaller angle, and I'm not having any luck, usually it should just be 90-77.6 to get 12.4 but the answer is wrong.