A shooter wants to fire a bullet in such a way that its horizontal range is equal to three times its maximum height. At the what angle should he fire the bullet to achieve this?
A
68o
B
53o
C
30o
D
45o
Verified Correct Answer: B.
Physical Principles & Numerical Solution
Horizontal range = 3 x maxi. height
=> (U2Sin2θ) / g = (3 x U2sin2θ) / 2g
∴sin2θ = 3sin2θ2
=> 2sinθcosθ = 3sin2θ2
∴ 4sinθcosθ = 3sin2θ
=> 4cosθ = 3sinθ
∴ sinθ/cosθ = 4/3; => tanθ = 4/3 = 1.3333
θ = tan-1 (1.3333)
= 53o
Source: Myschool Past Questions Archive (Record #14332)