Question

The magnitude of the velocity vector of the car is ∣∣v→∣∣ = 78 ft/s. If the vector v→ forms an angle θ = 0.09 rad with the horizontal direction, determine the Cartesian representation of v→ relative to the (iˆ, jˆ) component system.

Answer 1

`\vec{v} = (77.68~{\rm ft/s})\^i + (7.01~{\rm ft/s})\^j`

Step-by-step explanation:

The x- and y- components of the velocity vector can be written as following:

`\vec{v}_x = ||\vec{v}||\cos(\theta)\^i`

`\vec{v}_y = ||\vec{v}||\sin(\theta)\^j`

Since the angle θ and the magnitude of the velocity is given, the vector representation can be written as follows:

`\vec{v} = 78\cos(0.09)\^i + 78\sin(0.09)\^j\\\vec{v} = (77.68~{\rm ft/s})\^i + (7.01~{\rm ft/s})\^j`