In 5.20 h, a balloon drifts 6.5 km north, 2.00 km east, and 2.76 km in upward elevation from its release point on the ground.
(a) Find the magnitude of its average velocity.
. km/h
(b) Find the angle its average velocity makes with the horizontal.
. ° (above the horizontal)
To find the magnitude of the average velocity, you need to calculate the total displacement of the balloon in all three dimensions (north, east, and upward), and divide it by the time taken. Here's how you can do it:
1. Calculate the total displacement in the north direction. Since the balloon drifted 6.5 km north, the north component of displacement is 6.5 km.
2. Calculate the total displacement in the east direction. The balloon drifted 2.00 km east, so the east component of displacement is 2.00 km.
3. Calculate the total displacement in the upward direction. The balloon drifted 2.76 km in upward elevation, so the upward component of displacement is 2.76 km.
4. Calculate the net displacement by finding the vector sum of the north, east, and upward components. This can be calculated using the Pythagorean theorem as follows:
Net displacement = sqrt((north displacement)^2 + (east displacement)^2 + (upward displacement)^2)
In this case, the net displacement would be: sqrt((6.5 km)^2 + (2.00 km)^2 + (2.76 km)^2).
5. Finally, divide the net displacement by the time taken (5.20 h) to find the magnitude of the average velocity.
To find the angle that the average velocity makes with the horizontal, you can use trigonometry. Here's how you can do it:
1. Calculate the angle that the average velocity makes with the horizontal using the tangent function. The tangent of the angle can be calculated using the equation: tangent(angle) = (upward displacement) / (horizontal displacement).
In this case, the angle would be: angle = arctan((upward displacement) / (horizontal displacement)).
2. Use a calculator or trigonometric table to find the value of the angle.
By following these steps, you can find the answers to the given questions.