Question

A stone is released at rest from a height of $45m$ above the horizontal level ground. There is horizontal wind blowing due to whcih stone acquires an additional (in addition to acceleration due to gravity) horizontal acceleration of magnitude $10m/s^2$. Then the net distance traveled by stone before reaching ground is: (Take $g=10m/s^2$ and neglect air resistance)

• A. $45m$
• B. $45\sqrt{2}m$
• C. $45\sqrt{3}m$
• D. cannot be determined

Answer 1

The correct option is B $45\sqrt{2}m$

The time of flight will be given by $h=\frac{1}{2}g{t}^2$ so $t=\sqrt{\frac{2h}{g}}=3sec$

As the initial velocity is $zero$$soverticaldisplacementwillbe$y=\dfrac{1}{2}gt^2$ ...........(1)

And the horizontal displacement will be $x=\frac{1}{2}a{t}^2$ .....(2)

Putting value of $t^2$ from one to another lead us to $xg=ay$, which is an equation of $line$

so the path will be a $line$ and thus the net distance is nothing but net $displacement.$ which is nothing but $\sqrt{h^2+x^2}$

or $d=\sqrt{{45}^2+{45}^2}=45\sqrt{2}meter$