KVPY 2020-21 SA Exam Previous Papers

Question : 27 of 80

Marks: +1, -0

In a circus, a performer throws an apple towards a hoop held at 45 m height by another performer standing on a high platform (see figure below). The thrower aims for the hoop and throws the apple with a speed of 24 m/s. At the exact moment that the thrower releases the apple, the other performer drops the hoop. The hoop falls straight down. At what height above the ground does the apple go through the hoop?

21 m
22 m
23 m
24 m

Validate

Solution:

\tan \θ={45}/{25}

=9/5

\cos \θ={5}/{\√{106}}

By equation of trajectory

y=x \tan \θ-{1}/{2} g {x^{2}}/{u^{2} \cos ^{2} \θ}

h=25 \×{9}/{5}-{1}/{2} \×10 {(25)^{2}}/{(24)^{2} \×({5}/{\√{106}})^{2}}

h=45-{5 \×25 \×106}/{576}

h \≈ 22 {m}

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