a car moving with a velocity of 20m/s at 30 degree to the horizontal, what is the components of the velocity along the horizontal
the component of any vector V in direction x is
Vx = |V| cos theta
where |V| is the magnitude, 20 in this case, and theta is the angle between the Vector and the direction you want, in this case cos 30
That is the horizontal component. You did not give a horizontal direction (compass) angle so you can not do East and North components of that horizontal component .
To find the components of the velocity along the horizontal, we can use trigonometry. The velocity vector has two components: one along the horizontal (x-axis) and one along the vertical (y-axis).
Given that the car has a velocity of 20 m/s at an angle of 30 degrees to the horizontal, we can determine the component along the horizontal using the cosine function.
The formula to calculate the horizontal component of velocity is:
Horizontal Component = Velocity × cos(θ)
Where:
- Velocity is the magnitude of the velocity vector (20 m/s in this case)
- θ is the angle the velocity vector makes with the horizontal (30 degrees in this case)
So, substituting the given values into the formula:
Horizontal Component = 20 m/s × cos(30°)
Now, we can calculate the cosine of 30 degrees using a calculator or by referring to a trigonometric table. The cosine of 30 degrees is approximately 0.866.
Horizontal Component = 20 m/s × 0.866
Simplifying the equation gives us:
Horizontal Component = 17.32 m/s
Therefore, the horizontal component of the velocity is 17.32 m/s.