A projectile is launched from an origin (0cm,0cm) on a tilted plane. The plane makes 30 degrees with the horizontal. The launcher sends the ball with a speed of 0.2m/s.
At what angle should the projectile be launched to hit the target at (0.7m,0.6m) location?
Assume there are no resistive forces to the projectile motion in this plane.
r_f = r_i + v_i*t + 1/2at2
Breaking the velocity vector into it's x and y components:
v_y = vsinΘ
v_x = vcosΘ
The Attempt at a Solution
In the x-direction:
There is no acceleration in the x direction, so the above equation is reduced to:
x_f - x_i = vcosΘ*t
0.6 = vcosΘt
t = 0.3 / cosΘ (EQUATION 1)
In the y-direction:
y_f - y_i = vsinΘt - 4.9t2
0.7 = vsinΘt - 4.9t2 (EQUATION 2)
SUB EQUATION 1 INTO 2
0.7 = 0.2sinΘ (0.3/cosΘ) - 4.9(0.3/cosΘ)2
This is where I get stuck... solving the trigonometric equation. I can't find a solution, so I'm thinking that my above reasoning may be wrong.
Either that, or I am just having an incredibly hard time with trig -- which I've been out of practice for 8 years.
Any suggestions / guidance is very much appreciated.