A very broad elevator is going up vertically with a constant acce… - Vidyadip

MCQ

A very broad elevator is going up vertically with a constant acceleration of $2\,m / s ^2$. At the instant when its velocity is $4\,m / s$ a ball is projected from the floor of the lift with a speed of $4\,m / s$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return the floor is $..............\,s$ $\left(g=10\,m / s ^2\right)$

A
$\frac{1}{2}$
✓
$\frac{1}{3}$
C
$\frac{1}{4}$
D
$1$

✓

Answer

Correct option: B.

$\frac{1}{3}$

b
(b)

Let us see the motion relative to elevator,

$a_r=a_b-a_e=(-10)-(+2)=-12\,m / s ^2$

Now,

$T =\frac{2 u_y}{a_r}=\frac{2 \times u \sin \theta}{a_r}$

$=\frac{2 \times 4 \times \sin 30^{\circ}}{12}=\frac{1}{3}\,s$

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