Answers
To find the x, y, and z components of the vector [tex]\(\vec{A}\)[/tex] shown in the diagram, we need to use trigonometric relationships.
Here are the steps to calculate each component:
Step 1: Understand the 3D vector components
- The vector [tex]\(\vec{A}\)[/tex] in a 3D space has three components, [tex]\(A_x\)[/tex] along the x-axis, [tex]\(A_y\)[/tex] along the y-axis, and [tex]\(A_z\)[/tex] along the z-axis.
- The given angles provide the direction of the vector in the 3D coordinate system.
Step 2: Calculate the z-component [tex](A_z)[/tex]
- Use the cosine of the angle between the vector [tex]\(\vec{A}\)[/tex] and the x-y plane, which is given as 35°. The cosine of this angle gives the ratio of the adjacent side [tex](A_z)[/tex] to the hypotenuse [tex](\(|\vec{A}|\))[/tex]:
[tex]\[ A_z = |\vec{A}| \cdot \cos(35°) \][/tex]
Step 3: Calculate the projection of A on the x-y plane [tex](A_xy)[/tex]
- Use the sine of the same angle to find the length of the projection of [tex]\(\vec{A}\)[/tex] on the x-y plane: [tex]\[ A_{xy} = |\vec{A}| \cdot \sin(35°) \][/tex]
Step 4: Calculate the x-component [tex](A_x)[/tex] and y-component [tex](A_y)[/tex]
- Now, use the projection [tex]\(A_{xy}\)[/tex] and the angle in the x-y plane (55°) to find [tex]\(A_x\)[/tex] and [tex]\(A_y\)[/tex]:
[tex]\[ A_x = A_{xy} \cdot \cos(55°) \][/tex]
[tex]\[ A_y = A_{xy} \cdot \sin(55°) \][/tex]
Step 5: Apply the calculations
- [tex]\(|\vec{A}| = 65 \, m\)[/tex], and we can now plug this value into the equations to calculate [tex]\(A_x\), \(A_y\), and \(A_z\).[/tex]
Let's perform these calculations.
The components of the vector [tex]\(\vec{A}\)[/tex] are approximately:
-[tex]\( A_x = 21.38 \)[/tex] m (along the x-axis),
- [tex]\( A_y = 30.54 \)[/tex]m (along the y-axis),
- [tex]\( A_z = 53.24 \)[/tex] m (along the z-axis).
To find the x, y, and z components of the vector a, we need more information about the vector. Without the direction or angles, we cannot determine the x, y, and z components of the vector a. Please provide more information so that we can help you further.
Explanation:To find the x, y, and z components of the vector a, we need more information about the vector. From the given information, it seems that the magnitude of vector a is 65 m. However, the x, y, and z components of the vector require the direction or angles.
Without the direction or angles, we cannot determine the x, y, and z components of the vector a. Please provide more information so that we can help you further.
Related Questions
What percentage of Earth's water is found in glaciers?
Answers
Final answer:
Glaciers and ice caps hold about 68.7% of Earth's fresh water, with most freshwater being stored in Antarctica and Greenland. They are essential parts of the water cycle and are vital fresh water reserves that could be affected by global warming.
Explanation:
Approximately 68.7% of Earth's fresh water is contained within glaciers and ice caps, with the vast majority of that - 90% in Antarctica, 9% in Greenland, and the remaining 1% scattered in other alpine regions. Glaciers play a crucial role as they hold about 69% of the world's fresh water, highlighting their importance in the global water cycle and as reserves of fresh water. As the Earth's climate warms, these glaciers are melting at an accelerated pace, which could significantly affect water supplies and sea levels worldwide.
The distribution of water on Earth is predominantly in the oceans, with about 97% being salt water. Freshwater accounts for only 3% of the Earth's water, with glaciers and polar ice caps comprising most of this freshwater. The potential melting of this ice due to global warming poses a serious threat to coastal cities and freshwater systems.
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by υ⃗ =[5.00m/s−(0.0180m/s3)t2]i^ + [2.00m/s+(0.550m/s2)t]j^. Part A What is ax(t) the x-component of the acceleration of the car as function of time?