Question

The distance between a frog and an insect is $12\text{m}$ on a horizontal surface. The frog can jump with a maximum speed of $\sqrt{10}\text{m/s}$. The minimum number of jumps required by the frog to catch the insect is
$[$ Take $g=10{\text{m/s}}^2$ $]$

• A. $13$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is D $12$

For the minimum number of jumps, the horizontal range travelled by the frog should be maximum in one jump.
We know that the range is maximum when the angle of projection is ${45}^{\circ }$.

Range of a projectile,
$R=\frac{u^2\sin \left(2\theta \right)}{g}$
So, maximum range,
$R_{max}=\frac{u^2\sin (2\times {45}^{\circ })}{g}$
$\Rightarrow R_{max}=\frac{\left(\sqrt{10}{)}^2\sin \right(2\times {45}^{\circ })}{10}=1\text{m}$
So, number of jump required,
$n=$ distance to be covered $/$ distance can be covered in one jump
$\Rightarrow n=\frac{12\text{m}}{1\text{m}}=12$