Question 250 of 308

A helicopter is flying horizontally with a speed $v$ at an altitude $h$ has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped ?

A$\sqrt{\dfrac{2gh{v}^{2}+1}{{h}^{2}}}$B$\sqrt{2gh{v}^{2}+{h}^{2}}$C$\sqrt{\dfrac{2gh}{{v}^{2}}}+{h}^{2}$D$\sqrt{\dfrac{2{v}^{2}h}{g}+{h}^{2}}$

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Answer: (D) $\sqrt{\dfrac{2{v}^{2}h}{g}+{h}^{2}}$

The aeroplane imparts $v$ velocity to the food packet horizontally when dropping. Horizontal range of food packet $=v\times \sqrt{\dfrac{2h}{g}}$
Also, Horizontal distance, travelled by aeroplane $=v\times \sqrt{\dfrac{2h}{g}}$ thus, vertical distance between aeroplane and person $=h$
distance $=\sqrt{\dfrac{2{v}^{2}h}{g}+{h}^{2}}$