the range of projectile which start with velocity v with angle of elevation alpha is given by R=v2sin2@/g .find percantgae error in range due to an error of 1% g and error of 0.5% in alpha.
Answers
Given info : The range of projectile which starts with velocity v with angle of elevation α is given by R = v²sin2α/g.
To find : The percentage error in range due to an error of 1 % in g and error of 0.5 % in α.
solution : here, R = v²sin2α/g
To find error in R,
% error in R = 2 × % error in v + 2 cot2α × % error in α + % error in g
let angle of elevation, α = 30° [ it should be mentioned]
here % error in v = 0
% error in g = 1 %
% error in α = 0.5 %
so, % error in R = 0 + 2 × cot60° × 0.5 % + 1 %
= 2 × 1/√3 × 0.5 % + 1 %
= 0.577 % + 1 %
= 1.577 %
Therefore the percentage error in R is 1.577 % if angle of elevation is taken as 30°.
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