Question

An elevator without a ceiling is ascending up with an acceleration of $5{\text{ms}}^{-2}$. A boy on the elevator shoots a ball in vertical upward direction from a height of $2\text{m}$ above the floor of elevator. At this instant the elevator is moving up with a velocity of $10{\text{ms}}^{-1}$, and the floor of the elevator is at a height of $50\text{m}$ from the ground. The initial speed of the ball is $15{\text{ms}}^{-1}$ with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. ($g=10{\text{ms}}^{-2}$)

• A. $2.13\text{s}$
• B. $2.0\text{s}$
• C. $1.0\text{s}$
• D. $3.12\text{s}$

Answer 1

The correct option is A $2.13\text{s}$

Given: ${\overrightarrow{u}}_{LG}=+10\hat{j},{\overrightarrow{a}}_{LG}=S\hat{j}{\overrightarrow{u}}_{BL}=15\hat{j},{\overrightarrow{a}}_{BG}=-10\hat{j}{S}_{BL}=u_{BL}t+\frac{1}{2}{a}_{BL}{t}^2\Rightarrow -2=\left[15\right]t+\frac{1}{2}[-10-5]t^2\Rightarrow -4=30t-15t^2\Rightarrow 15t^2-30t-4=0t=\frac{-(-30)\pm \sqrt{900+4\left(60\right)}}{2\left(15\right)}t\approx 2.13\text{s}$