Question

Consider a fruit fly flying a room with velocity v(t) = < -sin(t), cos(t), 1 >

a. if the z = 1 + 2(pi) is the room's ceiling, where will the fly hit the ceiling?

b. if the temperature in the room is T(z) = 65 + (1/2)z² how quickly is the temperature increasing for the fly at time t = 2.

c. from the velocity, find the location of the fruit fly at time t if at t = pi the fly is at the point (0, 0, pi)

Answer 1

Given : v(t) = < -sin(t), cos(t), 1>

a) z = 1+ 2(pi)

when z = 1+2(pi), x = cos(2(pi) + 1) and y = sin(2(pi) +1). The fly will hit the ceiling at <0.9919,0.1268,2(pi)+1>

b)

at t = 2, z = 2. thus T'(2) = 2. The temperature is increasing at a rate of 2 units per second.

c)

In option a) since the initial values were not given we took the initial position as the origin and thus the constant of integral as 0. In this case