Question

A balloon is rising vertically at 12 ft. per second and being blown horizontally at 18 ft. per second. Find:

a) The angle its path makes with the horizontal.
b) Its actual velocity.

Answer 1

The angle the path makes with the horizontal is approximately 33.69 degrees. The actual velocity is approximately 22.97 ft/s.

Step-by-step explanation:

To find the angle the path makes with the horizontal, we can use the trigonometric relationship between the horizontal and vertical components of the velocity.

The angle can be found using the formula: angle = arctan(vertical velocity / horizontal velocity). In this case, the vertical velocity is 12 ft/s and the horizontal velocity is 18 ft/s. Substituting these values into the formula gives us: angle = arctan(12/18) = arctan(2/3) ≈ 33.69 degrees.

To find the actual velocity, we can use the Pythagorean theorem. The actual velocity is given by the square root of the sum of the squares of the horizontal and vertical velocities: velocity = sqrt(horizontal velocity^2 + vertical velocity^2).

In this case, substituting the given values gives us: velocity = sqrt(18^2 + 12^2) = sqrt(528) ≈ 22.97 ft/s.