Naval Battle Problem During the noon observation of June 3, 1810, HMS Surprise s

Question

Naval Battle Problem During the noon observation of June 3, 1810, HMS Surprise sails along the x-axis in pursuit of the French merchantman Buonaparte (also sailing along the x-axis, and 12 km ahead). Surprise is a faster ship and is gaining on Buonaparte at a rate of 240 m/hr. The maximum trajectory angle of the cannon aboard Surprise is 5 degree, and the muzzle speed of a shot is v_o = 700 m/s. Ignore air resistance. Determine the range of Surprise's cannon. Assuming the conditions above hold for the duration of the pursuit, at precisely what time will Surprise have Buonaparte in range.

Explanation / Answer

Range of surprise will be given by

R = (240/3600 + 700 cos (5)) (2* 700 sin (5)/10)

R= 8.5 km

So surprise should cover 12 - 8.5 km to reach the other ship in range

3.5 km at 240m/hr will take

14.58 hrs

this it will have it by 2 am in the midnight

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