A velocity of 30 mph is resolved into two components, each of which makes an angle of 45 degrees with it. Find their magnitude.
To find the magnitude of the two components, we can use trigonometry. Since the velocity is resolved into two components, we can represent it as a right-angled triangle. Let's call the two components A and B.
According to the given information, the velocity is 30 mph, and the angle between each component and the velocity is 45 degrees.
To find the magnitude of the components, we can use sine and cosine functions. The sine function relates the opposite side of an angle to the hypotenuse, and the cosine function relates the adjacent side to the hypotenuse in a right triangle.
In this case, we'll use the sine function for one component and the cosine function for the other component:
Component A:
sin(45°) = Opposite / Hypotenuse
sin(45°) = A / 30 mph
Rearranging the equation:
A = 30 mph * sin(45°)
Component B:
cos(45°) = Adjacent / Hypotenuse
cos(45°) = B / 30 mph
Rearranging the equation:
B = 30 mph * cos(45°)
Now, we can calculate the magnitudes of the components:
A = 30 mph * sin(45°)
≈ 21.21 mph
B = 30 mph * cos(45°)
≈ 21.21 mph
Therefore, the magnitude of both components is approximately 21.21 mph.
To find the magnitude of the components, we need to use trigonometry.
Let's call the magnitude of the components A and B.
Since both components make an angle of 45 degrees with the velocity vector, we can use the cosine function to find their magnitudes.
cos(45 degrees) = A / 30 mph
cos(45 degrees) = B / 30 mph
Using the cosine of 45 degrees, which is equal to 0.7071, we can solve for A and B:
A = 0.7071 * 30 mph
B = 0.7071 * 30 mph
A ≈ 21.21 mph
B ≈ 21.21 mph
Therefore, the magnitude of each component is approximately 21.21 mph.
sketch the diagram:
the normal sum of the components is zero.
V1*cos45-V2Cos45=0
so V1=V2
the sum in the direction of the 30 mph add, so
V1*sin45+V2*sin45=30
2V1*sin45=30
solve for V1