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.
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- 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)
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- 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)
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- 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.
