Question

A car is driving directly north on the freeway at a speed of 119 km/h and a truck is leaving the freeway driving 87.7 km/h in a direction that is 35° west of north. Assume north to be in the +y-direction and east to be in the +x-direction.
What is the magnitude of the velocity of the truck relative to the car?


What is the direction of the velocity of the truck relative to the car?

Answer 1

The magnitude of the velocity of the truck relative to the car is 183.9 km/h

The direction of the velocity of the truck relative to the car is 67 ⁰ north of west.

Velocity of the truck relative to the car

The velocity of the truck relative to the car is the resultant velocity of the vehicles.

The resultant velocity of the car is calculated as follows;

Vertical component of the velocity

Vyi = 119 km/h

Vy2 = 87.7 km/h x sin(35) = 50.3 km/h

Vy(total) = 119 km/h + 50.3 km/h = 169.3 km/h

Horizontal component of the velocity

Vx = -87.7 x cos(35) = -71.84 km

Resultant velocity

v = √Vy² + Vx²

v = √[(169.3²) + (-71.84)²]

v = 183.9 km/h

Direction of the velocity

θ = arc tan(Vy/Vx)

θ = arc tan(169.3 / -71.84)

θ = -67 ⁰

θ = 67 ⁰ north of west.

Thus, the magnitude of the velocity of the truck relative to the car is 183.9 km/h and the direction of the velocity of the truck relative to the car is 67 ⁰ north of west.

Learn more about resultant velocity here: brainly.com/question/24767211

#SPJ1