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Q.

Two particles are projected upwards with the same initial velocity v0 in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest points will be

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a

tan2⁡θ1

b

v0sin⁡θ1

c

v0/cos⁡θ1

d

v02sin2⁡θ1

answer is A.

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Detailed Solution

As the horizontal ranges are the same v02sin⁡2θ1g=v02sin⁡2θ2g or  sin⁡2θ1=sin⁡2θ2 or  2θ1=π−2θ2  or  θ1+θ2=π/2 Now  h1max=v0sin⁡θ122g and  h2max=v0sin⁡θ222g∴ h1maxh2max=sin⁡θ12sin⁡θ22=sin2⁡θ1cos2⁡θ1=tan2⁡θ1
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