Answer :
To find the y-component of a vector with a magnitude of 38 m/s at an angle of 85°, we can use trigonometry. The y-component of a vector is calculated using the sine of the angle. Here's a step-by-step solution:
1. Understand the Components of the Vector:
A vector can be broken down into two components: x (horizontal) and y (vertical). The y-component is found by using the magnitude of the vector and the sine of the angle from the horizontal.
2. Angle and Magnitude:
- Magnitude = 38 m/s
- Angle = 85°
3. Calculate the Y-Component:
- We will use the sine function because it relates the angle to the y-component in a right-angled triangle.
- The formula to calculate the y-component is:
[tex]\[ \text{y-component} = \text{magnitude} \times \sin(\text{angle}) \][/tex]
4. Perform the Calculation:
- Convert the angle from degrees to radians since trigonometric functions typically use radians in calculations.
- Calculate the sine of 85°.
- Multiply the sine of the angle by the magnitude of the vector.
5. Result:
The y-component of the vector, calculated using these steps, is approximately 37.9 m/s.
Therefore, the correct answer is 37.9 m/s.
1. Understand the Components of the Vector:
A vector can be broken down into two components: x (horizontal) and y (vertical). The y-component is found by using the magnitude of the vector and the sine of the angle from the horizontal.
2. Angle and Magnitude:
- Magnitude = 38 m/s
- Angle = 85°
3. Calculate the Y-Component:
- We will use the sine function because it relates the angle to the y-component in a right-angled triangle.
- The formula to calculate the y-component is:
[tex]\[ \text{y-component} = \text{magnitude} \times \sin(\text{angle}) \][/tex]
4. Perform the Calculation:
- Convert the angle from degrees to radians since trigonometric functions typically use radians in calculations.
- Calculate the sine of 85°.
- Multiply the sine of the angle by the magnitude of the vector.
5. Result:
The y-component of the vector, calculated using these steps, is approximately 37.9 m/s.
Therefore, the correct answer is 37.9 m/s.
