Solving 2D projectile motion problem for angle, given displacement and time.

[A. Sartorius]

- I need to find the appropriate launch angle that will land an object 65 meters north of my position. Therefore Δdx = 65m [N]
- I am told that the time the object take to hit the ground is 5.23 seconds. Therefore Δt = 5.23s
- I then used the equation Δdx = v1xΔt to find v1x = 12.43 m/s.

After this I haven't a clue what to do next. Would someone kindly outline the steps I need to take to find the launch angle. Muchas gracias.

 

[DukeLuke]

If you look at the projectile motion in the y (up) direction $$y = y_0 + v_{yo}t + \frac{1}{2}a t^2$$ the only variable you don't know is the initial velocity in the y direction $v_{yo}$. Can you express $v_{yo}$ in terms of the launch angle and v1x? In this case the equation can be solved for the launch angle.