a weather station releases a weather balloon.The balloon's buoyancy accelerates it upward at 15m/s sq.At the same time,a wind accelerates it horizontally to the right at 6.5m/s sq.What is the resulting acceleration
Well, it seems like that weather balloon is having a blast! With an upward acceleration of 15m/s sq and a horizontal acceleration of 6.5m/s sq, we can say that the resulting acceleration will be like a dance move — a combination of two different steps. Hence, the resulting acceleration will be the diagonal of a slightly wobbly triangle. So, grab your dancing shoes and get ready for some trigonometry! Using Pythagoras' theorem, we can calculate the magnitude of the resulting acceleration:
Resulting acceleration = √(15^2 + 6.5^2) m/s sq.
And there you have it, the magnitude of the resulting acceleration. Just keep in mind to dance your way through those number steps!
To find the resulting acceleration of the weather balloon, we can use vector addition. Since the accelerations are acting in different directions, we need to add them as vectors.
We have an upward acceleration of 15 m/s^2 and a horizontal acceleration to the right of 6.5 m/s^2. These can be represented as:
Upward acceleration: 0 m/s^2 + 15 m/s^2
Horizontal acceleration: 6.5 m/s^2 + 0 m/s^2
To add these vectors, we can use the Pythagorean theorem. The magnitude of the resulting acceleration is given by:
Resulting acceleration = √(upward acceleration^2 + horizontal acceleration^2)
Plugging in the values, we get:
Resulting acceleration = √((15 m/s^2)^2 + (6.5 m/s^2)^2)
Simplifying the equation:
Resulting acceleration = √(225 m^2/s^4 + 42.25 m^2/s^4)
= √267.25 m^2/s^4
Where the value of √267.25 is approximately 16.35.
Therefore, the resulting acceleration of the weather balloon is approximately 16.35 m/s^2.
To find the resulting acceleration, we need to combine the upward acceleration of the weather balloon due to buoyancy and the horizontal acceleration due to the wind.
The upward acceleration due to buoyancy is given as 15 m/s², and the horizontal acceleration due to the wind is given as 6.5 m/s² to the right.
Since the two accelerations are acting in perpendicular directions (vertical and horizontal), we can use the Pythagorean theorem to calculate the resulting acceleration. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (resultant) is equal to the sum of the squares of the other two sides.
So, let's calculate the resulting acceleration:
Resultant acceleration = √(upward acceleration^2 + horizontal acceleration^2)
Plugging in the values:
Resultant acceleration = √(15^2 + 6.5^2)
= √(225 + 42.25)
= √(267.25)
≈ 16.34 m/s²
Therefore, the resulting acceleration of the weather balloon is approximately 16.34 m/s².
a^2 = 15^2 + 6.5^2
a = 16.3
I expect you can determine the direction.