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Falling body When an object falling from rest encoun- ters air resistance proportional to the square of its velocity, the distance it falls (in meters) after f seconds is given by m d(t) = 쓰In ( cosh where m is the mass of the ob- m ject in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant. a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2. b. How long does it take her to fall the first 100 m? The sec- ond 100 m? What is her average velocity over each of these intervals?

Falling body When an object falling from rest encoun- ters air resistance proportional to the square of its velocity, the distance it falls (in meters) after f seconds is given by m d(t) = 쓰In ( cosh where m is the mass of the ob- m ject in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant. a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2. b. How long does it take her to fall the first 100 m? The sec- ond 100 m? What is her average velocity over each of these intervals?

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Falling body When an object falling from rest encoun- ters air resistance proportional to the square of its velocity, the distance it falls (in meters) after f seconds is given by m d(t) = 쓰In ( cosh where m is the mass of the ob- m ject in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant. a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2. b. How long does it take her to fall the first 100 m? The sec- ond 100 m? What is her average velocity over each of these intervals?
Transcribed Image Text:Falling body When an object falling from rest encoun- ters air resistance proportional to the square of its velocity, the distance it falls (in meters) after f seconds is given by m d(t) = 쓰In ( cosh where m is the mass of the ob- m ject in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant. a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2. b. How long does it take her to fall the first 100 m? The sec- ond 100 m? What is her average velocity over each of these intervals?
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