The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of 19.5 m/s in a direction of 65° north of west.
(a) What is the magnitude of the ostrich's velocity component that is directed due north?
1 m/s
(b) What is the magnitude of the ostrich's velocity component that is directed due west?
2 m/s
What on earth is your school subject?
(a) 19.5 sin 65 m/s = ?
(b) 19.5 cos 65 m/s = ?
To find the magnitude of the ostrich's velocity component that is directed due north, we need to determine the northward component of its velocity.
(a) To find the northward component, we need to use trigonometry. We can use the cosine function to find the component.
The northward component can be found using the formula: northward component = velocity * cosine(theta), where theta is the angle north of west.
northward component = 19.5 m/s * cos(65°)
northward component = 19.5 m/s * cos(65°) ≈ 8.32 m/s
Therefore, the magnitude of the ostrich's velocity component that is directed due north is 8.32 m/s.
(b) Similarly, to find the magnitude of the ostrich's velocity component that is directed due west, we need to use the sine function to find the component.
The westward component can be found using the formula: westward component = velocity * sine(theta), where theta is the angle north of west.
westward component = 19.5 m/s * sin(65°)
westward component = 19.5 m/s * sin(65°) ≈ 17.5 m/s
Therefore, the magnitude of the ostrich's velocity component that is directed due west is 17.5 m/s.
To find the magnitude of the ostrich's velocity component that is directed due north, we can use trigonometry.
The given velocity of the ostrich is 19.5 m/s at an angle of 65° north of west. To find the north component, we need to determine the component of the velocity that is parallel to the north direction.
We can find this component by using the formula:
North Component = Velocity * sin(angle)
Here, the angle is the angle between the velocity vector and the north direction, which is 90° - 65° = 25°.
Now, let's calculate the magnitude of the ostrich's velocity component that is directed due north:
North Component = 19.5 m/s * sin(25°) = 19.5 m/s * 0.4226 ≈ 8.26 m/s
Therefore, the magnitude of the ostrich's velocity component that is directed due north is approximately 8.26 m/s.
To find the magnitude of the ostrich's velocity component that is directed due west, we can use the same approach.
The west component is perpendicular to the north direction, so we can use the formula:
West Component = Velocity * cos(angle)
Here, the angle is still 65°.
Let's calculate the magnitude of the ostrich's velocity component that is directed due west:
West Component = 19.5 m/s * cos(65°) = 19.5 m/s * 0.4226 ≈ 16.35 m/s
Therefore, the magnitude of the ostrich's velocity component that is directed due west is approximately 16.35 m/s.