Question

An aeroplane moving horizontally with a speed of 200 m/s drops a food packet while flying at a height of 396.9 m. The time taken by the food packet to reach the ground and its horizontal range is ...

A.5 s and 1000 m
B.9 s and 1800 m
C.8 s and 1600 m

Answer 1

Alright so. They give us the velocity vector but we need find the horizontal and vertical components of the vector. Luckily for this problem, the velocity vector is really just the horizontal component with a component of 0j for vertical initial velocity.

So let’s find time using the kinematic equations:
Yf = Yi + Viyt + 1/2at^2
-396.9 = 0t - 4.9t^2
I multiplied gravity by 1/2 and brought the initial height to the left side

So now we have -4.9t^2 = -396.9
Divide both sides by -4.9 and take the square root of the answer to find time. I got 9 seconds

Now plug this information into the horizontal displacement equation for projectile motion:
Xf = Xi +Vixt
Xf = 200(9)
Xf = 1800 meters