CBSE Class 11-science Answered
the maximum height attained by a projectile is increased to 4% by changing the angle of projection without changing the speed of the projectile.The percentage increase in the time of flight will be
2%
10%
15%
20%
Asked by pushpakumari291279 | 06 Dec, 2020, 04:11: PM
Expert Answer
Let u be projection velocity, θ be the angle of projection
Maximum height , h = (u2 /2g) sin2θ
let us consider , sinθ = α
Hence we have Maximum height as , h = (u2 /2g) α2 ................ (1)
if we differentiate above equation , we get , dh = ( u2 / 2g ) 2 α dα ................. (2)
If we divide eqn.(2) with eqn.(1) , we get , ( dh / h ) = 2 ( dα / α ) ............ (3)
From eqn.(3) , we see that, if maximum height is increased by 4 % , then α is increased by 2%
Time of flight , T = [ (2 u )/ g ] sinθ = [ (2 u )/ g ] α
Hence Time of flight is directly proportional to α
If maximum height is increased by 4 % , then α is increased by 2% . Hence time of flight also is increased by 2%
Answered by Thiyagarajan K | 06 Dec, 2020, 08:15: PM
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