a bullet fires from a rifle attain a maximum height of 25m crosses a range of 200m .find the angle of projection
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Hmax = H = 25m
Range = R = 200m
H = u²sin²Ɵ/2g
25 = u²sin²Ɵ/2×10
25×20 = u²sin²Ɵ
500 = u²sin²Ɵ --------(1)
R = u²sin2Ɵ/g
200×10 = u²sin2Ɵ
2000 = u²sin2Ɵ---------(2)
divide equation 1 by 2
500/2000 = u²sin²Ɵ/u²sin2Ɵ
0.25 = sin²Ɵ/sin2Ɵ
we know sin2Ɵ = 2sinƟ × cosƟ
0.25×2 = tanƟ
0.5 = tan Ɵ
Ɵ = 26.5°
Range = R = 200m
H = u²sin²Ɵ/2g
25 = u²sin²Ɵ/2×10
25×20 = u²sin²Ɵ
500 = u²sin²Ɵ --------(1)
R = u²sin2Ɵ/g
200×10 = u²sin2Ɵ
2000 = u²sin2Ɵ---------(2)
divide equation 1 by 2
500/2000 = u²sin²Ɵ/u²sin2Ɵ
0.25 = sin²Ɵ/sin2Ɵ
we know sin2Ɵ = 2sinƟ × cosƟ
0.25×2 = tanƟ
0.5 = tan Ɵ
Ɵ = 26.5°
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