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A ball is threown straight upward with a speed v from a point h meters above the ground.Show that the time taken for the ball to strike the ground is (v/g)[1+ sqrt{1+(2hg/v^2)}].

A ball is threown straight upward with a speed v from a point h meters above the ground.Show that the time taken for the ball to strike the ground is (v/g)[1+ sqrt{1+(2hg/v^2)}].

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

Taking the vertically upwards direction as positive, for the entire motion, the displament of the ball iss=-h. Initial velocity of ball isu=+vand acceleration isa=-g

Sinces=ut+\dfrac{1}{2}at^2

\implies -h=vt-\dfrac{1}{2}gt^2
\implies t^2-\dfrac{2v}{g}t-\dfrac{2h}{g}=0
\implies t=\dfrac{v}{g}+\sqrt{\dfrac{v^2}{g^2}+\dfrac{2h}{g}} =\dfrac{v}{g}(1+\sqrt{1+\dfrac{2gh}{v^2}})

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