SOLUTION: Precalculus Michael Sullivan Section 1.1 Q. 68 A hot-air balloon, headed due east at an average speed of 15 mph and at a constant altitude of 100 feet, passes over an inter

This problem is for 3D space (x,y,z).

In this problem, we have a point (x,y,z) moving uniformly (with constant speed) in 3D space over x-axis
in its positive direction at the constant height z = 100 feet.


From the context, time t is in seconds and t=0 is when the point is precisely over the intersection.


Thus, for y-coordinate, we have y(t) = 0.


For z-coordinate, we have z(t) = 100 feet.


For x-coordinate we have (making conversion from miles per hour to feet per second)

    x(t) = 15 mph * t seconds =  =  feet.


To write the expression for the distance d(t), use the distance formula in 3D

    d(t) = sqrt(x^2(t) + y^2(t) + z^2(t)) =  =  feet.


At this point, the problem is solved completely and the final expression for the distance is obtained.


ANSWER.  The distance from the balloon to the intersection in time t seconds is d(t) =  feet.