a car travels east at 89 km/h for 1 hour.it then travels 26 east of north at 141 km/h for another 1 hour.
a)what is the average speed for the trip?
b)what is the average velocity for the trip?
a. d = 89 + 141km[64o[]CCW.
d = 89 + 141*Cos64 + i141*sin64
d = 89 + 61.8 + 126.7i = 150.8 + 126.7i
= 196.9km[40o]
Speed = d/t = 196.9km/2h = 98.4km/h.
b. V = 196.9km[40o]/2h = 98.4km/h[40o].
= 98.4km/h[50o] E of N.
To find the average speed for the trip, you need to calculate the total distance traveled divided by the total time taken.
For the first hour, the car travels east at 89 km/h. So the distance traveled in the first hour is 89 km/h * 1 h = 89 km.
For the second hour, the car travels 26 degrees east of north at 141 km/h. To find the distance traveled, we need to use trigonometry. We can calculate the horizontal component of the distance traveled by multiplying the velocity (141 km/h) by the cosine of the angle (26 degrees). The horizontal component is 141 km/h * cos(26) = 126.94 km.
Therefore, the total distance traveled is 89 km + 126.94 km = 215.94 km.
The total time taken for the trip is 1 hour + 1 hour = 2 hours.
To find the average speed, we divide the total distance traveled by the total time taken: Average speed = Total distance / Total time = 215.94 km / 2 h = 107.97 km/h.
So, the average speed for the trip is 107.97 km/h.
To find the average velocity for the trip, we need to take into account both the magnitude and direction of the displacement.
In the first hour, the car travels east, so its displacement is only in the east direction. Therefore, the displacement in the first hour is 89 km to the east.
In the second hour, the car travels 26 degrees east of north, so its displacement has both a north and east component. Using trigonometry, we can calculate the vertical (north) component of the displacement by multiplying the velocity (141 km/h) by the sine of the angle (26 degrees). The vertical component is 141 km/h * sin(26) = 61.35 km.
The horizontal (east) component of the displacement is still 126.94 km as calculated earlier.
Therefore, the total displacement is 89 km east + 126.94 km east + 61.35 km north.
To find the average velocity, we divide the total displacement by the total time taken: Average velocity = Total displacement / Total time = (89 km + 126.94 km + 61.35 km) / 2 h.
To calculate the direction of the average velocity, we can use trigonometry. The angle for the average velocity can be found using the formula tan(theta) = (total north displacement) / (total east displacement).
tan(theta) = 61.35 km / 215.94 km = 0.28472.
theta = atan(0.28472) = 15.22 degrees.
Therefore, the average velocity for the trip is (89 km + 126.94 km + 61.35 km) / 2 h at a direction of 15.22 degrees north of east.