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Irina-Kira [14]

2 years ago

8

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?

1 answer:

blsea [12.9K]2 years ago

3 0

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.

<h3>Velocity of the truck relative to the car</h3>

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;

<h3>Vertical component of the velocity</h3>

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

<h3>Horizontal component of the velocity</h3>

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

<h3>Resultant velocity</h3>

v = √Vy² + Vx²

v = √[(169.3²) + (-71.84)²]

v = 183.9 km/h

<h3>Direction of the velocity</h3>

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

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