Question

A cart is moving at 55 m/s at an angle of 25° to the ground. Determine the horizontal component.

Answer 1

The horizontal component of the velocity is 49.85 m/s.

Step-by-step explanation:

Rectangular Components of a Vector

A 2D vector can be expressed in several forms. The rectangular form gives its two components, one for each axis (x,y). The polar form gives the components as the pair (r,θ) being r the magnitude and θ the angle.

When the magnitude and angle of the vector are given, the rectangular components are calculated as follows:

`v_x=v\cos\theta`

`v_y=v\sin\theta`

Where v is the magnitude of the vector and θ is the angle with respect to the x positive direction.

The cart is moving at v=55 m/s at θ=25°, thus:

`v_x=55\cos 25^\circ`

`v_x=49.85\ m/s`

The horizontal component of the velocity is 49.85 m/s.