Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ign
ored) from their low-flying planes and scoring points for having the weights land close to a target. a plane 70 m above the ground is flying directly toward a target at 44 m/s . at what distance from the target should the pilot drop the weight?
The movement of the weight can be decomposed in a vertical component and a horizontal component.
The vertical movement is uniformly accelerated motion (constant acceleration) and is the one that we will use to find the time of flight (t). The initial vertical speed is zero, and the vertical distance (y) traveled is 70 m. The acceleration is that of gravity.
y = 1/2 . a. t²
t = √(2y/a) = √(2 . 70 m/ 9.8 m/s²) = 3.8 s
The horizontal movement is a uniform motion (constant speed). The horizontal speed is that of the plane. The horizontal distance at what the pilot should drop the weight is:
This example of the effect of volume on the pressure of a given amount of a confined gas is true in general. Decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure.