Question

A truck travels up a hill with a 7.5◦incline.The truck has a constant speed of 24 m/s.What is the horizontal component of thetruck’s velocity?Answer in units of m/s.005 (part 2 of 2) 10.0 pointsWhat is the vertical component of the truck’svelocity?Answer in units of m/s.

Answer 1

The horizontal component of the truck's velocity is: 23.70 m/s

The vertical component of the truck's velocity is: 3.13 m/s

Step-by-step explanation:

You have to apply trigonometric identities for a right triangle (because the ramp can be seen as a right triangle where the speed is the hypotenuse), in order to obtain the components of the velocity vector.

The identities are:

Cosα=
`(CA)/(H)`

Senα=
`(CO)/(H)`

Where H is the hypotenuse, α is the angle, CA is the adjacent cathetus and CO is the opposite cathetus

The horizontal component of the truck's velocity is:

Let Vx represent it.

In this case, CA=Vx, H=24 and α=7.5 degrees

Vx=(24)Cos(7.5)

Vx=23.79 m/s

The vertical component of the truck's velocity is:

Let Vy represent it.

In this case, CO=Vy, H=24 and α=7.5 degrees

Vy=(24)Sen(7.5)

Vy=3.13 m/s