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Question

The army is testing out a new prototype artillery cannon with an uncommonly high muzzle velocity of 1000 m/sec . The design bugs haven't been fully worked out yet, so the cannon has to wait at least a full minute between shots (reloading, etc.). The cannon can be aimed with an angle between 0 and 90 degrees with respect to the horizontal.

A particularly demanding exercise is being conducted, in which the cannon fires an initial shot into the air, and while the first shell is still in the air, a second shot is fired (at a different angle) so that both shells impact the target (at ground level) simultaneously.

What is the maximum horizontal distance from the cannon to the target, such that this is possible?

Details and Assumptions:

Assume level ground, with no air resistance.
The gravitational acceleration is 10 m/s².
Give your answer in meters, to the nearest whole meter.
For the sake of this problem, ignore the Earth's curvature.

Answer 1

For a time lag of k seconds (k>=60),
y1 = 1000sinθ t - 10t^2
x1 = 1000cosθ t

y2 = 1000sinØ (t-k) - 10t^2
x2 = 1000cosØ (t-k)

Since maximum range for y1 is achieved at θ=45°, k must be less than 70.2 seconds.

see what you can do with that.

Answer 2

maximum time in air is when the ball gets to maximum height, or when θ=90°, so the vertical speed is v=100-10t=0 at t=10, making total flight time 20 seconds.

There is no way to wait at least a minute for the 2nd shot while the 1st is still up in the air.