A body thrown is vertically up with a velocity ‘U ’from ground. It reaches the maximum height ‘H’ in ‘t’ seconds. Then the correct statement among the following is
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a
At a height H2 from ground its velocity is 'U'2
b
At time t its velocity is ‘U’
c
At a time 2t its velocity is ‘-U’
d
At a time 2t its velocity is ‘-6U’
answer is C.
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Detailed Solution
a) we know for vertical projection , h=U22g=maximum height reached by a body V2−U2=2as; here v is final velocity;u is initial velocity; a is acceleration ; s is displacement; At half of maximum height , put height=h2⇒V2−U2=2gh2substitute h=U22g⇒V2−U2=−gU22g⇒V2−U2=−U22⇒V2=−U22+U2⇒V=U2b) At time ‘t’ the body is in maximum height its velocity is zero. ‘t’ is time of ascent t=Ug c) we know,V=U+ at time of ascent is t=Ug, for vertically projected body →a=−g substitute time =2t in v=u+at V=U+2at substitute time of ascent=t=Ug ⇒V=U+2−gUg V=U−2U ⇒V=−U =velocity of the body after time =2t