Question

Sneha throws a pillow up into the air which returns to her hands after $3\text{s}$. Then pick out the correct statements from the following.

• A. After $2\text{s}$, the pillow is at a height of $6.4\text{m}$.
• B. The pillow reaches a maximum height of $11\text{m}$.
• C. After $2\text{s}$, the pillow is at a height of $9.8\text{m}$.
• D. The pillow is thrown up with a velocity of $14.7\text{m}{\text{s}}^{-1}$.

Answer 1

Answer: (B), (C), (D)

The correct options are
B The pillow reaches a maximum height of $11\text{m}$.
C After $2\text{s}$, the pillow is at a height of $9.8\text{m}$.
D The pillow is thrown up with a velocity of $14.7\text{m}{\text{s}}^{-1}$.

Given:
Total time taken by the pillow to go up and fall back into Sneha's hands, $\text{T}=3\text{s}$
When the pillow is at its highest position in the air, its velocity, $\text{v}=0$
The pillow takes equal time for going up and falling down $⟹$ Time taken for the upward journey, ${\text{t}}_1=\frac{\text{T}}{2}=1.5\text{s}$

From bottom to top point:
Using the first equation of motion,
$\text{v}=\text{u}-\text{gt}$
$0=\text{u}-9.8\times 1.5$
$\text{u}=9.8\times 1.5=14.7\text{m}{\text{s}}^{-1}$

From bottom to top point:
Using the second equation of motion,
$\text{s}=\text{ut}-\frac{1}{2}{\text{gt}}^2$
$s=14.7\times 1.5-0.5\times 9.8\times (1.5{)}^2$
$s\approx 11\text{m}$

For first 2 s of motion:
Using the second equation of motion,
$\text{s}=\text{ut}-\frac{1}{2}{\text{gt}}^2$
$\text{s}=14.7\times 2-0.5\times 9.8\times (2{)}^2$
$\text{s}=9.8\text{m}$