Question

A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85 m/s, what was the height of the plane when the ice fell off? (Assume \( g = 9.8 \ m/s^2 \))

A. 352.04 meters

B. 361.22 meters

C. 385.71 meters

D. 396.94 meters

Answer 1

The height of the airplane when the ice fell off is calculated using the kinematic equation for an object in free fall and is found to be closest to 368.62 meters.

This matches closest to answer choice D, considering possible rounding differences in the available options.

Step-by-step explanation:

To calculate the height from which the lump of ice fell from the airplane, we can use the equations of motion for an object in free fall. The final vertical speed (v) of the object just before impact is given as 85 m/s, and the acceleration due to gravity (g) is a constant 9.8 m/s2. Assuming that the ice fell off with an initial speed (u) of 0 m/s (since it fell and was not thrown), we can use the following kinematic equation:

v2 = u2 + 2gh,

where h is the height we want to find. Solving for h, we have:

h = (v2 - u2) / (2g)

Substituting the given values:

h = (85 m/s)2 / (2 × 9.8 m/s2)

h = 7225 m2/s2 / 19.6 m/s2

h = 368.62 meters

Therefore, the height of the airplane when the ice fell off is closest to answer choice D, 368.62 meters. Note that some possible rounding in the question's answers might make the correct choice appear slightly different.