Question

Suppose that the speed v (in ft/s) of a skydiver t seconds after leaping from a plane is given by the equation 𝑣 = 190(1 − 𝑒 − 0.168𝑡).

(a) Graph 𝑣 versus 𝑡.

(b) By evaluating an appropriate limit, show that the graph of 𝑣 versus 𝑡 has a horizontal asymptote 𝑣 = 𝑐 for an appropriate constant 𝑐.

(c) What is the physical significance of the constant 𝑐 in part (b)?

Answer 1

$$v(t)=190(1-e^{-0.168t})$$

(a)

(b)

$$\lim\limits_{t\to\infin}v(t)=\lim\limits_{t\to\infin}(190(1-e^{-0.168t}))=190(ft/s)$$

The horizontal asymptote is $v=190\ ft/s.$

(c) It is the terminal velocity of skydiver.