How High and At What Angle Should Person B Shoot to Hit Person A?

[gen.nutville]

Homework Statement

Person A is shot out of cannon at 100m/s at 30 degrees above the horizontal on top of a 75 meter tall cliff. After 3 seconds, Person B, standing next to the cannon, shoots an arrow at 200m/s at Person A. At what height does the arrow strike person A, and what angle did he fire at?

Homework Equations

X_Ay=75+200 sin⁡(θ) (t-3)+g/2 〖(t-3)〗^2
X_Ax=200 cos⁡(θ) (t-3)
X_By=75+50t+g/2 t^2
X_By=86.6t

The Attempt at a Solution

{(75+200sin(θ)(t-3)+g/2(t-3)^2)^2 + (200cos(θ)(t-3))^2}^1/2 = {(75+50t+g/2 t^2)^2 + (86.6t)^2}^1/2

For some reason I am unable to isolate theta

 

[Doc Al]

Make use of the fact that A and B must have the x and y coordinates when they collide.

 

[baba89]

and solve for it.

I would suggest using trigonometric identities to simplify the equations and make it easier to isolate theta. Additionally, it may be helpful to plot the equations on a graph to visualize the problem and potentially find a solution. It is also important to consider the assumptions made in the equations, such as neglecting air resistance and assuming constant acceleration due to gravity. These assumptions may affect the accuracy of the solution. Another approach could be using vector analysis to find the angle at which the arrow is fired and the height at which it strikes Person A. It is also important to double check the units and make sure they are consistent throughout the calculations. Overall, it may be helpful to break down the problem into smaller, more manageable parts to find a solution.