40 m Vo=141 m/s 1500 m - An Israeli patrol boat off the coast of the Gaza strip

Question

40 m Vo=141 m/s 1500 m - An Israeli patrol boat off the coast of the Gaza strip is ordered to destroy a Hamas rocket launcher that sits on the roof of 40-meter tall building in Gaza City. The horizontal distance between the boat and the rocket launcher is 1500 meters. The muzzle velocity of the patrol boat's stabilized 30-mm cannon is 141 meters/second. What are the two angles (relative to the horizontal) at which the patrol boat's gun can be aimed in order to destroy the rocket launcher? Express your answer in degrees to a precision of three significant figures. [You may ignore air resistance. Assume an acceleration of gravity of precisely 9.800 m/s. Your answers must be accurate to within 0.3 degrees in order to receive credit. You must also show your work.

Explanation / Answer

in horizontal,

v0x t = dx

141 cos(theta) t = 1500

t cos(theta) = 10.638 ........ (i)

In vertical,

40 = (141 sin(theta)) t - 9.8 t^2 / 2

40 = 1500 tan(theta) - 554.55 / (cos^2(theta))

theta = 65.8 deg Or 25.8 deg

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