Question

Pochinki, a city in the Erangel map of PUBG, is one of the deadliest places to drop. A novice player, in lure of maximum loot aims to have a drop at Pochinki is released from a helicopter flying horizontally at a constant velocity of 40 m$s^{-1}$. How far from the city of Pochinki (in km), horizontally, the player needs to drop if the helicopter is flying at a height of 180m from the ground. [g=10$m/s^2$]

Answer 1

Hint: The question can be solved using basic Newton's laws and second equation of motion. The key here is that if an object moves with a (horizontal) velocity or falls freely, time for the fall remains the same for both. Both reach the ground at the same time.

Complete step by step answer:
If the player has to reach the specified spot (consider a point), we need to calculate the trajectory that the dropped player will make, so that before some distance, we can drop the player from the plane and player still can move ahead with the previous velocity (due to inertia) and reach our spot i.e. Pochinki.
Consider a rough sketch:

If the player is dropped at a distance d from Pochinki, he will continue to experience the helicopter velocity along the same direction therefore. This happens so because an object in motion or rest continues the same unless acted upon by some force externally.
Now, we are given that g=10m$s^{-2}$, height =180m.
So, the object takes about same time to reach the ground as for free fall, we may write:
$s=ut+\dfrac{1}{2} gt^2$
$180=0.t+\dfrac{1}{2} 10\times t^2$
$\dfrac{180}{5}=t^2$
t=6s
(From second law of motion.)
We get the time t= 6s.

Thus, to get our distance d, we know,
Velocity x time = distance
Therefore,
$d=40 \times 6 m$
d=240m

Thus, the player should be dropped at a distance of 240m from Pochinki so that it makes to Pochinki just in time.

Note: One might get lost if one might not be aware of the fact that the time to reach the ground is exactly the same even if we have a horizontal velocity. This is important information which might not come intuitively sometimes.