Question

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22. MAINIDEA The skydiver shown in Figure 13 falls at a constant speed in the spread-
eagle position. Immediately after opening the parachute, is the skydiver accelerating? If
so, in which direction? Explain your answer using Newton's laws.

Answer 1

Yes, upward

Step-by-step explanation:

We can solve the problem by using Newton's second law, which can be written as

`\sum F = ma`

where
`\sum F` is the net force, m is the mass, a is the acceleration.

At the beginning, the skydiver is falling at constant speed (called terminal velocity): this means that the two forces acting on him/her, the weight W (downward) and the air resistance R (upward) are equal in magnitude, and so the net force (and the net acceleration) is zero:

`R-W=ma=0 \rightarrow R-W`

When the parachute is opened, the resistance force suddenly increased (because the surface area of the body increases), so Newton's second law becomes:

`R-W=ma`

this time,
`R>W`, therefore
`a>0`, which means that the acceleration has the same direction as the air resistance (upward). As a result, the skydiver will accelerated upward, which means that its vertical velocity will decrease in magnitude (because he/she was travelling downward, so the acceleration is in the opposite direction).