The drawing shows an exaggerated view of a rifle that has been ‘sighted in\' for

Question

The drawing shows an exaggerated view of a rifle that has been ‘sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v0 = 375 m/s, there are the two possible angles 1 and 2 between the rifle barrel and the horizontal such that the bullet will hit the target. One of these angles is so large that it is never used in target shooting. Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identity may be useful: 2 sin cos = sin 2.)

Explanation / Answer

Using projectile equation,

y = h + x·tan - g·x² / (2v²·cos²)
where, y = height

= 0 m

h = initial height = 0 m
x = horizontal dist = 91.4 m

v = speed = 375 m/s

0 = 0 + 91.4*tan - 9.81*(91.4)² / (2(*375)²*cos²)
0 = 91.4tan - 0.291 /cos²

0 = 91.4tan - 0.291 sec²
0 = 91.4tan - 0.291 - 0.291 tan²
0.291tan² - 91.4tan + 0.291 = 0

tan = 314.09

tan = 0.003184

(a) arctan0.00403891 = 0.1824º

(b) arctan247.592 = 89.818º

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