Question

2. Fighter airplane is flying horizontally at the altitude h=5000 m with velocity of u=100 m/s. When airplane passes directly above an air defense station, the battery fires a gun to intercept the airplane as shown on the picture. Initial velocity of the projectile V0 = 500 m/s. Disregarding air resistance, find the following: a) at which angle  to the horizonal should the gun fire to hit the target? b) what is the time t until the impact? c) what is the horizontal distance s from the gun to the point of impact?

Answer 1

here is the diagram attached

Answer 2

please someone help!!!!!

Answer 3

i'm in desperate need of help!!!!

Answer 4

For the bullet to intercept the plane, the bullet's horizontal speed must be equal to the plane's speed. \(\LARGE V_{0}cos(\alpha) = u\). So, \(\LARGE \alpha = cos^{-1}\frac{u}{V_{0}}\)
Now taking motion in vertical direction, initial vertical speed of bullet = \(\LARGE V_{0}sin(\alpha)\), height to be covered = h, acceleration = -g,
So,
\(\LARGE h = V_{0}sin(\alpha)t - \frac{1}{2}gt^{2}\)
Solve to get the value of t

Horizontal distance s = speed of plane * time taken = \(u*t\)

Answer 5

thankyou!