A car is traveling at a speed of 55 mph with a bearing of 210°. What vector represents the velocity?
the vector (55cos210° , 55sin210°)
27.5
To represent the velocity of the car as a vector, we need to consider both the magnitude (speed) and the direction (bearing).
Given that the car is traveling at a speed of 55 mph, the magnitude of the velocity vector is 55.
To determine the direction, we use the bearing of 210°. Bearings are typically measured clockwise from the north direction in degrees.
To convert this bearing to a vector, we can use trigonometry. We can represent the vector as the sum of its horizontal and vertical components using the sine and cosine functions.
To find the horizontal component of the vector, we can use the cosine function. The horizontal component is given by:
horizontal component = magnitude × cos(angle)
Substituting the values, we get:
horizontal component = 55 × cos(210°)
To find the vertical component of the vector, we can use the sine function. The vertical component is given by:
vertical component = magnitude × sin(angle)
Substituting the values, we get:
vertical component = 55 × sin(210°)
Therefore, the velocity vector can be represented as:
velocity = (horizontal component, vertical component)
By calculating the horizontal and vertical components, we can find the velocity vector.