- #1
ishterz
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Homework Statement
An anti aircraft gun with initial velocity 400m/s at angel theta above the horizontal, and the shells may be assumed to move freely under gravity. The target is a pilotless aircraft which flies at a speed of 100m/s directly towards the gun at a constant height of 3500m. A shell fired from the gun hits the aircraft when it is at a horizontal distance of 'x' m from the gun.
By using equation of trajectory show
x^2tan^2(theta)- (32000)xtan(theta) + (x^2 + 1.12x10^8) = 0
Homework Equations
Equation of trajectory: y = xtan(theta) - gx^2/ (V^2 cos^2 (theta))
The Attempt at a Solution
I assumed the y distance for both will be the same on collision, since the aircraft's height is constant
For the shell, I did :
x = 400cos(theta) t
therefore t= x/400cos(theta)
v= 400sin(theta)t - 5t^2
I subsituted for t in the second equation and tried to solve but could not get the answer.
Please help!
Thank you for your time