Gwapo O.

asked • 10/02/18# Formula that predicts the location of moving enemy

A rocket that explodes not on impact, but explodes on a timer will be shot from myself to the enemy. The timer can only be inputted at the start of the shot. The rocket can only go straight and has a speed of 1500m/s . The enemy is moving in a straight line at a 135 degree angle with a speed of 400m/s. The distance between myself and my enemy is 5000m. I need a formula that predicts the precise time until the rocket should explode so that it will explode directly on my enemy's location.

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## 1 Expert Answer

Arturo O. answered • 10/03/18

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Assumptions:

All motion occurs in the x-y plane, and it is a horizontal plane.

The rocket launches from the origin (0,0)

Rocket moves only in a straight line at speed v = 1500 m/s

Initial position of target: (x

_{0},y_{0}). In this problem, x_{0}= 5000, y_{0}= 0.Direction target moves: θ (above +x axis). In this problem, θ = 135°.

Speed of target: u. In this problem, u = 400 m/s

You need to solve for the time-to-target t and a launch angle φ for the rocket, above the x-axis. At time t, the rocket and target must arrive at the same point, so

x-coordinate of intercept point:

(v cosφ)t = x

_{0}+ (u cosθ)ty-coordinate of intercept point:

(v sinφ)t = y

_{0}+ (u sinθ)tYou have to solve a system of 2 equations in 2 unknowns t and φ:

(v cosφ)t = x

(v sinφ)t = y

_{0}+ (u cosθ)t(v sinφ)t = y

_{0}+ (u sinθ)tThis is not a linear system, so it may need to be solved by numerical methods or graphing methods.

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Arturo O.

10/02/18