A military submarine is 1000 miles away from its target. It launches a missle th

Question

A military submarine is 1000 miles away from its target. It launches a missle that travels at a constant velocity of v= 400 mi/h. There is a wind speed of W= 20 mph in the positive y direction, that pushes the missle off course, however the missle continually redirects and points towards the target. Write an equation for its trajectory. I was having issues uploading an image of the problem, however the trajectory looks like an upside down parabola, with one end being at (1000,0) where the submarine is and the other end being the target at (0,0)

Explanation / Answer

Vx^2 + Vy^2 = 400   actual speed of rocket
Vx = (400^2 - 20^2)^1/2     using the vector triangle
Vx = 20 * (400 - 1)^1/2 = 20 * 399^1/2    speed of rocket along the x-axis
x = Vx * t   = 399.5 * t     position of rocket at time t
Note that the problem implies that rocket always travels along the x-axis

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