What is the direction and magnitude of the net force acting on the hot air balloon? It has an arrow up with 6300, an arrow down with 3200, an arrow to the right of 1350 and an arrow left with 745.
Is this how to do it and if so, how do I convert the sin of theta into degrees.
6300-3200=3100 up
1350-605=745 right
31002+7452=x2
approximately 3188.26
745/3188.26=.234
Yeah, you have the right process.
After you calculate the net force in x and y directions, construct a right triangle by drawing your vectors head-to-tail.
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theta
The hypotenuse has a length of ~3188 by Pythagorean theorem.
To calculate the angle, we use trig.
tan(theta) = opposite / adjacent
theta = arctan(745 / 3100) = 13.5 deg
So your final answer is 3188N @ 13.5 degrees [East of North].
thank you
X = 1350-745 = 605 N.
Y = 6300-3200 = 3100 N.
Fn = Sqrt(X^2+Y^2) = Sqrt(605^2+3100^2) = 3158.5 N.
Tan A = Y/X = 3100/605 = 5.12397.
A = 79o N. of E. = Direction.
To determine the direction and magnitude of the net force acting on the hot air balloon, you need to break down the forces into their horizontal and vertical components.
First, calculate the horizontal and vertical components of the forces:
Vertical component: 6300 - 3200 = 3100 (upward force)
Horizontal component: 1350 - 745 = 605 (rightward force)
Next, use the Pythagorean theorem to find the magnitude of the net force:
Magnitude of net force = √(vertical component^2 + horizontal component^2)
Magnitude of net force = √(3100^2 + 605^2)
Magnitude of net force ≈ 3188.26 units
Now, to convert the sine of theta into degrees, you need to use the inverse sine function (also known as arcsine). If you have the value sin(theta), you can use the arcsine function to find the angle in radians. To convert radians to degrees, simply multiply the value by 180/π (approximately 57.3 degrees).
In your case, you mentioned sin(theta) = 0.234. To find theta in degrees, follow these steps:
1. Calculate the arcsine of 0.234:
theta (in radians) = arcsin(0.234)
2. Convert the value from radians to degrees:
theta (in degrees) ≈ theta (in radians) * (180/π)
By following these steps, you can determine the angle in degrees based on the given sine value.