Example 17 The Acceleration of a Skydiver

A skydiver is falling straight down, along the negative y direction. (a) During the initial part of the fall, her speed increases from 16 to 28 m/s in 1.5 s, as in Figure 2.25a. (b) Later, her parachute opens, and her speed decreases from 48 to 26 m/s in 11 s, as in part b of the drawing. In both instances, determine the magnitude and direction of her average acceleration.

(a) A skydiver falls initially with her parachute unopened. (b) Later on, she opens her parachute. Her acceleration is different in the two parts of the motion. The initial and final velocities are v
0 and v, respectively.

Figure 2.25 (a) A skydiver falls initially with her parachute unopened. (b) Later on, she opens her parachute. Her acceleration is different in the two parts of the motion. The initial and final velocities are v ₀ and v, respectively.

Is her average acceleration positive or negative when her speed is increasing?

Since her speed is increasing, the acceleration vector must point in the same direction as the velocity vector, which points in the negative y direction. Thus, the acceleration is negative.

Is her average acceleration positive or negative when her speed is decreasing?

Since her speed is decreasing, the acceleration vector must point opposite to the velocity vector. Since the velocity vector points in the negative y direction, the acceleration must point in the positive y direction. Thus, the acceleration is positive.

Solution

(a)

Since the skydiver is moving in the negative y direction, her initial velocity is v₀

–16 m/s and her final velocity is v

–28 m/s. Her average acceleration

is the change in the velocity divided by the elapsed time:

(2.4)

As expected, her average acceleration is negative. Note that her acceleration is not that due to gravity (–9.8 m/s²) because of wind resistance.

(b)

Now the skydiver is slowing down, but still falling along the negative y direction. Her initial and final velocities are v₀

–48 m/s and v

–26 m/s, respectively. The average acceleration for this phase of the motion is

(2.4)

Now, as anticipated, her average acceleration is positive.