Question

A balloon is released 4 feet away from an observer. The balloon is rising vertically at a rate of 3 ft/sec and at the same time the wind is carrying it horizontally away from the observer at a rate of 4 ft/sec. At what speed is the angle of inclination of the observer’s line of sight changing 4 seconds after the balloon is released?

Answer 1

The speed at which the angle of inclination of the observer's line of sight is changing 4 seconds after the balloon is released is 5 ft/sec.

Step-by-step explanation:

To find the speed at which the angle of inclination of the observer's line of sight is changing, we can use the concept of relative velocity. The vertical speed of the balloon is 3 ft/sec, while the horizontal speed due to the wind is 4 ft/sec. By using the Pythagorean theorem, we can find the total speed at which the balloon is moving relative to the observer.

The total speed is given by:

Speed = sqrt((vertical speed)^2 + (horizontal speed)^2)

Plugging in the values, we get:

Speed = sqrt((3 ft/sec)^2 + (4 ft/sec)^2) = sqrt(9 ft^2/sec^2 + 16 ft^2/sec^2) = sqrt(25 ft^2/sec^2) = 5 ft/sec.