Question

A grasshopper can jump a maximum horizontal distance of $40cm$. If it spends time on the ground then in this case its speed along the horizontal road will be:

• A. $1m/s$
• B. $2m/s$
• C. $\sqrt{2}m/s$
• D. $2\sqrt{2}m/s$

Answer 1

The correct option is C $\sqrt{2}m/s$

$\text{Step 1 : Expression for the range of a projectile}$

(Taking upward direction as positive)

Horizontal range is given by:

$R=\frac{u^2\sin 2\theta }{g}$ $....\left(1\right)$

$\text{Step 2: Calculation of initial speed u}$

$R=R_{max}=0.40m$

R is maximum at $\theta ={45}^o$ ;

Putting values in eq $\left(1\right)$

$0.40m=\frac{u^2\times \sin {90}^o}{10m/s^2}$

$\Rightarrow$ $u^2=4$

$\Rightarrow$ $u=2m/s$

$\text{Step 3 : Horizontal component of velocity}$

Speed along the horizontal road is the horizontal component of velocity.

Horizontal component of velocity $=u\cos \theta =u\cos {45}^o=2\times 1/\sqrt{2}=\sqrt{2}m/s$

Hence, option $\left(C\right)$ is correct answer.