NTSE Stage 2 SAT 2018 Exam Question Paper

Question : 29 of 100

Marks: +1, -0

A ball is thrown vertically up from the point A (see figure). A person,standing at a height H on the roof a of a building, tries to catch it, He misses the catch, the ball overshoots and simultaneously the person starts a stop-watch.
The ball reaches its highest point and he manages to catch it upon its return. By this time, a time interval T has elapsed as recorded by the stop-watch. If g is the acceleration due to gravity at this place, the speed with which the ball was thrown from point A will be:

$√{gH}+gT$
$\;\;{(√{g^{2}T^{2}+4gH})}/{2}$
$\;\;{(√{g^{2}T^{2}+8gH})}/{2}$
$(√{g^{2}T^{2}+2gH})$

Validate

Solution:

v=u-g(T/2)(v=0)

⇒u'=\;\;{gT}/{2}

{v}^{2}={u}^{2}+2g{H}

({u}')^{2}={u}^{2}-2{gH}

\;\;{g^{2}T^{2}}/{4}+2gH=u^{2}

u=\;\;{√{g^{2}T^{2}+8gH}}/{2}

Go to Question:

Prev Question

Next Question