(4%) Problem 7: Gun sights are adjusted to aim high to compensate for the effect

Question

(4%) Problem 7: Gun sights are adjusted to aim high to compensate for the effect of ravitv, effectively making the gun accurate only for a specific range If a gun is sighted to hit targets that are at the same height as the gun and 95 m away at the same height, how low, as a positive number in meters, will the bullet hit if aimed directly at a target 150 m away? The muzzle velocity of the bullet is 275 m/s. Grade Summa Deductions Potential ry 090 100% cos0 sin0 cotan0asin acos0 atan0 acotan sinhO cosh0 tanh cotanh0 tan Submissions Attempts remaining: ^6 1% per attempt) *1 2 3 detailed view END Degrees Radians CLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: Feedback: 1% deduction per feedback.

Explanation / Answer

R = v0^2 sin(2 theta) / g

95 = 275^2 sin(2 theta) / 9.8

sin(2 theta) = 0.0123

2 theta = 0.705

theta = 0.35 deg

now x = 150 m

t = x/ v cos(theta) = 0.5455 sec

y = v0 t + a t^2 /2

y = (275 sin0.35)(0.5455) - (9.8 x 0.5455^2 / 2)

y = 0.56 m .......Ans

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