A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 150m above the glacier at a speed of 110m/s.
How far short of the target should it drop the package?
To determine how far short the plane should drop the package, we need to calculate the horizontal distance the package will travel during its fall.
First, let's find the time it takes for the package to fall. We can use the formula for vertical motion:
h = 0.5 * g * t^2
where h is the vertical distance (150m) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Solve for t:
t = sqrt(2h / g) = sqrt(2 * 150m / 9.8m/s^2) ≈ 5.08s
Next, calculate the horizontal distance traveled using the equation:
d = v * t
where v is the horizontal velocity of the plane (110m/s) and t is the time it takes for the package to fall. Thus:
d = 110m/s * 5.08s ≈ 558.8m
Therefore, the plane should drop the package about 558.8 meters short of the target.