A projectile is to be projected towards enemy territory at the same horizontal level. The initial velocity of the projectile is known to be 100 ± 1 m / s . Initial angle of the projectile is known to

Question

A projectile is to be projected towards enemy territory at the same horizontal level. The initial velocity of the projectile is known to be 100 ± 1 m / s . Initial angle of the projectile is known to be 4 5 ∘ ± 1 ∘ with horizontal. What is the possible range of the projectile?

TestHub · Accepted Answer

The range of a projectile is given by R = g v 2 s i n ( 2 θ ) ​ . With v = 100 ± 1 m/s and θ = 4 5 ∘ ± 1 ∘ , we find the range. Maximum range: v = 101 m/s, θ = 4 6 ∘ . R ma x ​ = 9.81 ( 101 ) 2 s i n ( 9 2 ∘ ) ​ ≈ 1020 m. Minimum range: v = 99 m/s, θ = 4 4 ∘ . R min ​ = 9.81 ( 99 ) 2 s i n ( 8 8 ∘ ) ​ ≈ 980 m. Therefore, 980 m ≤ R ≤ 1020 m .

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