An airplane flies at 40 m/s at an altitude of 50 meters.The pilot drops a heavy package which falls to the ground.Where,approximately,does the package land relative to the plane's new position?
A)beneath the plane
B)400 m behind the plane
C)500 m behind the plane
D)more than 500 m behind the plane
E)none of these

Question

Quizplus · Accepted Answer

Assuming no air resistance, the horizontal velocity of the package remains the same as that of the plane, i.e., 40 m/s. However, the vertical velocity of the package is given by v = gt, where g is the acceleration due to gravity (9.8 m/s^2) and t is the time. Using the formula h = 1/2 gt^2 to find the time taken for the package to hit the ground, we get t = sqrt(2h/g) = sqrt(2*50/9.8) = 3.19 seconds (rounded to two decimal places). In this time, the plane would have traveled a horizontal distance of 40 m/s x 3.19 s = 127.6 meters. Therefore, the package would land beneath the plane, or at most, a negligible distance behind it (depending on how high above the ground the package was released). Hence, the answer is A) beneath the plane.

An Airplane Flies at 40 M/s at an Altitude of 50