# A balloon is rising at 3.6 m/s at same time is blown by wind for 5.4 m/s from east. Find the actual velocity and direction of the balloon.

## X = -5.4 m/s.

Y = 3.6 m/s.

Tan Ar = Y/X = 3.6/-5.4 = -0.66666
Ar = -33.7o = Reference angle.
A = -33.7 + 180 = 146.3o = Direction.

V = X/Cos A = (-5.4)/Cos146.3 = 6.49 m/s[146.3o].

## Well, that balloon certainly knows how to get some airtime! Let's calculate the actual velocity and direction, shall we?

First, we need to break down the balloon's motion. It is rising at 3.6 m/s vertically, and being blown 5.4 m/s horizontally from the east. Now, it's time for a little math!

To find the actual velocity, we can use the Pythagorean theorem. Let's square those speeds and add them up: (3.6^2 + 5.4^2) = 12.96 + 29.16 = 42.12.

Now, we just need to take the square root of that sum: √42.12 ≈ 6.49 m/s. So, the actual velocity of the balloon is approximately 6.49 m/s.

As for the direction, we can determine it using the tangent function: tanθ = (rise)/(run) = (3.6)/(5.4) = 0.67.

Taking the inverse tangent of 0.67, we find that the angle is roughly 33.7 degrees. Therefore, we can say that the balloon is rising at an angle of about 33.7 degrees from the vertical.

So, to sum it up, the actual velocity of the balloon is approximately 6.49 m/s in a direction about 33.7 degrees from the vertical. That balloon is really going with the flow and rising to new heights, quite literally!

## To find the actual velocity and direction of the balloon, we need to combine the vertical velocity (caused by the balloon rising) and the horizontal velocity (caused by the wind blowing).

Given:
Vertical velocity of the balloon (rising): 3.6 m/s
Horizontal velocity of the wind (eastward): 5.4 m/s

To calculate the actual velocity of the balloon, we can use the Pythagorean theorem, which states that the square of the hypotenuse (actual velocity) is equal to the sum of the squares of the other two sides (vertical and horizontal velocities).

Using the formula:
Actual velocity^2 = Vertical velocity^2 + Horizontal velocity^2

Substituting the values:
Actual velocity^2 = (3.6)^2 + (5.4)^2
Actual velocity^2 = 12.96 + 29.16
Actual velocity^2 = 42.12

Taking the square root of both sides:
Actual velocity = √42.12
Actual velocity ≈ 6.49 m/s

Therefore, the actual velocity of the balloon is approximately 6.49 m/s.

To find the direction of the balloon, we need to use trigonometry. The angle θ can be calculated by taking the inverse tangent (tan^-1) of the ratio of the vertical velocity to horizontal velocity.

θ = tan^-1 (Vertical velocity / Horizontal velocity)
θ = tan^-1 (3.6 / 5.4)
θ ≈ 33.69 degrees

Therefore, the actual direction of the balloon is approximately 33.69 degrees (measured from the east, clockwise).

So, the actual velocity of the balloon is approximately 6.49 m/s, and its direction is approximately 33.69 degrees (measured from the east, clockwise).

## To find the actual velocity and direction of the balloon, we need to combine the velocities of the balloon rising vertically and the wind blowing horizontally.

The velocity of the balloon rising vertically is given as 3.6 m/s, and the velocity of the wind blowing horizontally is given as 5.4 m/s from the east.

To combine these velocities, we can use vector addition. Since the velocity of the balloon is acting in the vertical direction and the wind is acting in the horizontal direction, we can think of the vertical and horizontal components of the velocity as two perpendicular sides of a right triangle.

Using the Pythagorean theorem, we can find the magnitude of the actual velocity:

Actual velocity = sqrt((vertical velocity)^2 + (horizontal velocity)^2)
= sqrt((3.6 m/s)^2 + (5.4 m/s)^2)
= sqrt(12.96 m^2/s^2 + 29.16 m^2/s^2)
= sqrt(42.12 m^2/s^2)
≈ 6.49 m/s

So, the magnitude of the actual velocity of the balloon is approximately 6.49 m/s.

To find the direction of the balloon, we can use trigonometry. The direction can be determined by finding the angle between the actual velocity vector and a reference direction (e.g., north, east, etc.). In this case, the reference direction is east since the wind is blowing from the east.

The direction can be found using the tangent function:

tan(theta) = (vertical velocity)/(horizontal velocity)
theta = arctan((vertical velocity)/(horizontal velocity))

theta = arctan(3.6 m/s / 5.4 m/s)
theta = arctan(0.6667)
theta ≈ 33.69 degrees

So, the actual velocity of the balloon is approximately 6.49 m/s in a direction of 33.69 degrees from east.