# Physics

A car heads due west on Interstate 80 going 63.0 km/hr for 2.1 hours. The car then turns and heads exactly northwest on Interstate 42 going 53 km/hr for 3.3 hours. What is the resultant displacement of the car?

I've done some work on it and I have a good idea. I found the total distance traveled for each direction, which is 63 * 2.1 = 132.3km for the first and 53 * 3.3 = 174.9km for the second.

Northwest = 45 degrees

Then, the cos(45)*174.9 = 123.67. That must be the length of each of the sides for the triangle with 174.9 as its hypotenuse.

Finally, the total bottom distance must be 132.3 + 123.67 =255.97

sqrt of 255.97^2 + 123.67^2 = 284.28 km. Is this correct?

1. 👍
2. 👎
3. 👁
1. west distance
= 63*2.1 + 53 (sqrt2/2)*3.3
= 255.97 right
north distance
= 53*(sqrt2/2)*3.3
= 123.67 right

so 284.28 is correct for the DISTANCE
NOT DISPLACEMENT'
Distance is scalar , km
Displacement is vector , distance AND direction
tan (angle north of west) = 124/256
so
angle north of west = 25.8 degrees

1. 👍
2. 👎
2. Note
always do orthogonal (perpendicular) components of vectors like x and y or north and west. Do not fool around with northwest, split it up into north component and west component immediately. Otherwise you will be doing trig forever.

1. 👍
2. 👎
3. @Damon, just one question. Sorry, but I'm not sure where you got the 124 and 256 from.

1. 👍
2. 👎

## Similar Questions

1. ### Physics

A 2500kg car is travelling due west at 30m/s when the brakes are applied, exerting a force of 5000 N [E]. What is the car's acceleration due to the braking?

2. ### Physics

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and was approaching at 9.00 m/s due south. The second car has a mass of 700 kg and was approaching at 15.0 m/s due west. (a)

3. ### Physics

Question: A Toyota car travelled at the rate of 70 km/hour leaves the house 2 hours after a Kia car has left and overtakes it in 5 hours. at what rate was Kia car travelling? What's the Formula pls? Thanks

4. ### Trigonometry

At t = 0 a car is due 2 km north of you heading west moving 13 km/s after 1.5 s. What is the angle in radians between you and the car from where the car was at t = 0?

1. ### physics

A car starts 200 m west of the town square and moves with a constant velocity of 15 m/s toward the east. a.Write the equation that represents the motion of the car. b.Where will the car be 10 minutes later? c.When will the car

2. ### Physics

Need Help with physics! Two cars drive on a straight highway. At time t = 0, car 1 passes mile marker 0 traveling due east with a speed of 17.0 m/s. At the same time, car 2 is 1.3 km east of mile marker 0 traveling at 30.0 m/s due

3. ### Physics

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at 8.00 m/s due south. The second car has a mass of 850 kg and is approaching at 17.0 m/s due west. (a)

4. ### algebra 2

A car enters an interstate highway 15 mi north of a city.The car travels due north at an average speed of 62.5 mi/h.Write an equation to model the carâ€™s distance d from the city after traveling for h hours. Graph the equation

1. ### Word Problem Maximizing A Bonus

Pauline Wong spends 4 hours selling a used car and 6 hours selling a new car. She works no more than 40 hours per week. In order to receive a bonus, she must sell at least one used car and four new cars each week. In that case,

2. ### Physics

A car is driving on a level highway. It is acted upon by the following forces: a downward gravitational force of 12 kN, an upward contact force due to the road of 12 kN, another contact force due to the road of 7 kN directed West,

3. ### Physics

1. Two people are pushing a disabled car. One exerts a force of 200 N East, the other a force of 250 N East. What is the net force exerted on the car? 2. Two hockey players strike a puck simultaneously from opposite sides. Red #3

4. ### Physics

A car sounding its horn (rated by the manufacturer at 600 Hz) is moving at 20 m/s toward the eat. A stationary observer is standing due east of the oncoming car. a) What frequency will he hear assuming that the speed of sound is