First slide

Rectilinear Motion

Question

A body is projected upwards with a velocity u. It passes through a certain point above the ground after t₁. The time after which the body passes through the same point during the return journey is

Moderate

A

$(\frac{u}{g} - t_{1}^{2})$
B

$2 (\frac{u}{g} - t_{1})$
C

$3 (\frac{u^{2}}{g} - t_{1})$
D

$3 (\frac{u^{2}}{g^{2}} - t_{1})$

Solution

Suppose v be the velocity attained by the body after time t₁.
Then $v = u - g t_{1}$ …..(i)
Let the body reach the same point at time t₂. Now velocity will be downwards with same magnitude v. Then
$\begin{array}{l} - v = u - g t_{2} . . . . . . (i i) \\ (i) - (ii) \Rightarrow 2 v = g (t_{2} - t_{1}) \\ or t_{2} - t_{1} = \frac{2 v}{g} = \frac{2}{g} (u - g t_{1}) = 2 (\frac{u}{g} - t_{1}) \end{array}$

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