Why Does the Recoiling Cannon's Projectile Angle Calculation Seem Incorrect?

[Ara macao]

A circus cannon, which has a mass M = 4500 kg, is tilted at q = 30°. When it shoots a projectile at v0 = 60 m/s with respect to the cannon, the cannon recoils along a horizontal track at vcannon = 0.5 m/s with respect to the ground.

a) At what angle to the horizontal does the projectile move with respect to the ground?

I get tan $$\theta$$ = 60sin30 / (0.5+60cos30). But it's still wrong. Can someone tell me what I did wrong? Thanks

 

[daniel_i_l]

In this question the horizontal momentum is conserved, so you know that the final momentum of the cannon equals the final horizontal momentum of the projectile.
are you sure that you don't know the mass of the projectile? If you knew the mass then with that you could find the horizontal velocity and then the angle.

 

[quicknote]

There could be a few potential issues with your calculation. First, make sure you are using the correct values for the angle q and the initial velocity v0. Also, double check that you are using the correct units for all variables (meters vs. degrees). Additionally, make sure you are using the correct formula for calculating the angle, as it may vary depending on the specific problem.

If you are still having trouble, try breaking down the problem into smaller steps and double checking each calculation along the way. It may also be helpful to consult with a peer or your instructor for further guidance.