A rescue plane drops a package of emergency rations to a stranded explorer. The plane is travelling horizontally at 40 m/s and at a height of 100m above the ground. Where does the package hit the ground relative to the point it was released?

Answer 1

We can use the kinematic equations to solve this problem. The key equation we need is:

y = vi*t + 1/2*a*t^2

where y is the vertical displacement (i.e. the height above the ground), vi is the initial velocity (which is zero when the package is released), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time elapsed.

We can use this equation to find the time it takes for the package to hit the ground:

100 = 0 + 1/2*(-9.8)*t^2
t = sqrt(2*100/9.8) = 4.52 s

Now we can use the horizontal velocity of the plane (40 m/s) and the time elapsed (4.52 s) to find the horizontal distance travelled by the package:

x = vi*t + 1/2*a*t^2
x = 40*4.52 = 181.04 m

So the package hits the ground 181.04 m horizontally away from the point it was released.