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Question

A particle is projected from the ground with velocity u at an angle θ with horizontal. The horizontal range, maximum height and time of flight are R, H and T respectively. They are given by, R=u2sin2θg,H=u2sin2θ2g and T=2usinθg
Now keeping u as fixed, θ is varied from 30 to 60. Then

A
R will first increase then decrease, H will increase and T will decrease
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B
R will first increase then decrease while H and T both will increase
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C
R will decrease while H and T will increase
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D
R will increase while H and T will increase
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Solution

The correct option is B R will first increase then decrease while H and T both will increase
From 30 to 60, sinθ increases
T=2usinθg
sin2θ will also increase from 30 to 60
H=u2sin2θ2g will also increase
As 30<θ<6060<2θ<120.
So, sin2θ will increase from 60 to 90 but decreases from 90 to 120
R=u2sin2θg will first increase and then decrease.

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