You are in possession of a compressed air cannon that shoots frozen chickens wit

Question

You are in possession of a compressed air cannon that shoots frozen chickens with incredible accuracy. You notice that 1.00×10^2 m downrange there is a crate of wolverines that is about to be hoisted straight up by a crane. Inexplicably, you know that the crate will be raised at a constant velocity of 10.0 m/s. Not wanting to miss this golden opportunity, you set up your cannon such that it's muzzle is exactly level with the crate and has a launch angle of 30.0 degrees with respect to horizontal. What magnitude of launch velocity should you use to hit the crate?

Explanation / Answer

For the both to hit, its vertical and horizontal co-ordinates should match.

x = (ucos30) t

=> 100 = (ucos30) t

=> t = 115.47/u

also, vertical distance covered by the crate in the same time => y = vt = 10t

this will be equal to the vertical distance of the projectile.

y = 10t = (usin30) t - (1/2)(9.8)t2

=> 10t = 57.735 - 4.9t2

=> 4.9t2 + 10t - 57.735 = 0

solving this gives two values of t of which the negative value of t (t = - 4.601s) is discarded since time t must remain positive.

t = 2.56 s

substitute this in t = 115.47/u

=> u = 45.10 m/s.

this is the magnitude of the launch velocity of the crate.

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