Scenario

A golf ball dropped from a tall building travels along a vertical line, experiencing significant air resistance along the journey. Sketch the ball’s *v-t*, *s-t* and *a-t *graphs.

Solution

- Since this motion involves only downward velocity, the “
**downward is positive**” sign convention is adopted.

–

- At the instant the ball is dropped, the ball experiences only its own weight
*mg*. The acceleration at that instant is thus *g*.
- Once the ball is moving, air resistance
*R* kicks in to reduce the acceleration.
- Since
*R* increases with speed, the acceleration eventually reaches zero when *R* matches *mg*.
- (Strictly speaking, the acceleration only approaches zero asymptotically as the ball only approaches terminal velocity asymptotically)

–

- At the instant the ball is dropped, the speed of the ball increases at the rate of 9.81 m s
^{-2}.
- As air resistance kicks in, the speed of the ball increases at decreasing rate, eventually reaching the terminal velocity.
- (Strictly speaking, the ball only approaches terminal velocity asymptotically)

–

- As the ball speeds up, the
*s-t* graph becomes steeper and steeper.
- The steepness stops increasing when the ball reaches terminal velocity. The
*s-t* graph becomes a straight line whose gradient is equal to the terminal velocity.

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