The drawing shows an exaggerated view of a rifle that has been ½sighted in\' for

Question

The drawing shows an exaggerated view of a rifle that has been ½sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v0 = 417 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

The range of a projectile is R=v2Sin2/g=2v2sincos/g

2v2sincos/g=91.4

sin2=5.15*10-3

This is valid for 2 values of which are and 90- since Sin2 and Sin (180-2) are equivalent.

a) Smaller =0.1476 degrees

b) Larger =90-0.1476=89.8524 degrees.

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