Finding the average velocity of a car traveling at different speeds and angles

AI Thread Summary
To find the average velocity of a car traveling at different speeds and angles, the car first travels east at 95 km/h for 1.5 hours, then at 30° east of north at 111 km/h for 1.8 hours. The calculations involve using the law of cosines to determine the resultant distance and angle. Initial attempts at solving the problem included incorrect distance and angle calculations, which were clarified by including units in the calculations. Ultimately, the correct approach led to a better understanding of the average velocity.
Intrusionv2
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Homework Statement



A car travels east at 95 km/h for 1.5 hours. It then travels 30.0° east of north at 111 km/h for 1.8 hours.

What is the average velocity for the trip? (Magnitude and degrees)

Homework Equations



law of cosines/resultant

The Attempt at a Solution



I have tried doing this:
d=952 + 1112 - 2(85*111)cos60 = 110km
v=110km / 3.3 hr = 33.1 m/s

for the angle...
tanx = Bsinx/ a + bcosx = 111sin60/95+111cos60 = 0.638
x = 32.5 north of east

Both of these were wrong...any help please??
 
Last edited:
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Intrusionv2 said:
d=852 + 1112 - 2(85*111)cos60 = 170.23km
You have basically the right idea to use the law of cosines, but this step is wrong. If you include the units in the calculation, you will see why.
 
diazona said:
You have basically the right idea to use the law of cosines, but this step is wrong. If you include the units in the calculation, you will see why.

Nvm, I see now.
 
Last edited:

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