Determine angle for gun to be shot at

[mmn]

Homework Statement

A toy gun fires marbles with a velocity v = 7m/s

a) to hit a toy soldier that is 1.8 m away and 1.1 m higher than the gun, at what angle should the gun be aimed?

b) Now assume that the toy soldier is dropped ( starting from rest) the instant the gun is fired. If the gun is aimed at the toy soldier when it is fired, at what height above the ground will the soldier be when it is hit by the bullet?

Homework Equations

a) Vx = 7cosx
Vy = 7sinx

1.8 = 7cosxt ...so... t = 1.8/(7cosx) (x component)
1.1 =7sinxt -4.9t^2 ( y component)

The Attempt at a Solution

a) wouldn't you just plug t into equation two and solve? that's what i did but I am getting
1.1cos^2x - 1.8 *cosx * sinx = -0.324

how do i solve for x if i am only permitted to use a regular calculator?

b) wouldn't b) be the same process but you would need to solve for the time at which they would hit?

 

[rl.bhat]

1.1cos^2x - 1.8 *cosx * sinx = -0.324
You can rewright the above equation as:

1.1 = 1.8*tanx - 0.324*sec^2x
1.1 = 1.8*tanx - 0.324*(1+tan^2x)
Now solve for tanx by using quadratic equation formula

 

[mmn]

Thanks!