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Question:

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is:

R4g

2Rg

Rg

R2g

Solution:

Correct option is C. 2Rg
Range will be same for time t1 t2 so angles of projection will be θ '90°-θ'
t1=2usinθ/g
t2=2usin(90°-θ)/g
and R=u²sin2θ/g
t1t2=4u²sinθcosθ/g²=2g[2u²sinθcosθ/g]=2Rg