A hot-air balloon is 160 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi/hr (88 ft/s). If the balloon rises vertically at a rate of 10 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 8 seconds later? Let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon. Write an equation relating x, y, and z. Differentiate both sides of the equation with respect to t. dy 0*+0%-0² dt dx dt = dz dt The rate of change of the distance between the motorcycle and the balloon after 8 seconds is about (Round to two decimal places as needed.)
A hot-air balloon is 160 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi/hr (88 ft/s). If the balloon rises vertically at a rate of 10 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 8 seconds later? Let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon. Write an equation relating x, y, and z. Differentiate both sides of the equation with respect to t. dy 0*+0%-0² dt dx dt = dz dt The rate of change of the distance between the motorcycle and the balloon after 8 seconds is about (Round to two decimal places as needed.)
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:A hot-air balloon is 160 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi/hr (88 ft/s). If the balloon
rises vertically at a rate of 10 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 8 seconds later?
Let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the
balloon. Write an equation relating x, y, and z.
Differentiate both sides of the equation with respect to t.
dx
+
=
dz
dt
The rate of change of the distance between the motorcycle and the balloon after 8 seconds is about
(Round to two decimal places as needed.)
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