KVPY 2020-21 SA Exam Previous Papers

Question : 23 of 80

Marks: +1, -0

Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is 30º and its maximum height is h, then the maximum height of other will be

1 h
3 h
6 h
10 h

Validate

Solution:

For range to be equal, angles of projection are complementary

\∴\θ_{1}=30°

\θ_{2}=90°-30=60°

h_{1}={u^{2} \sin ^{2}(\θ_{1})}/{2 g}=h \⇒{u^{2}}/{8 g}=h

For second ball

h_{2}={u^{2} \sin ^{2}(\θ_{2})}/{2 g}={3 u^{2}}/{8 g}=3 h

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