Question

work each of the following problems. show all work.

1. a jogger runs 6 km north, 5 km east, then another 4 km north. her average speed 8 km/h. how long will it take her to complete her run?

1. using the information from the previous question, what is her average velocity during this time?

Explanation:

Question 9

Step1: Calculate total distance

The jogger runs 6 km north, 5 km east, and 4 km north. Total distance \( d = 6 + 5 + 4 = 15 \) km.

Step2: Use speed formula to find time

Speed formula is \( v=\frac{d}{t} \), so \( t = \frac{d}{v} \). Given \( v = 8 \) km/h, \( t=\frac{15}{8}=1.875 \) hours.

Step1: Find displacement

Northward displacement: \( 6 + 4 = 10 \) km. Eastward displacement: 5 km. Displacement \( s=\sqrt{10^{2}+5^{2}}=\sqrt{100 + 25}=\sqrt{125}=5\sqrt{5}\approx11.18 \) km.

Step2: Find time from Q9

Time \( t = 1.875 \) hours.

Step3: Calculate average velocity

Average velocity \( v_{avg}=\frac{s}{t}=\frac{5\sqrt{5}}{1.875}\approx\frac{11.18}{1.875}\approx5.96 \) km/h (direction: \( \theta=\arctan(\frac{5}{10})=\arctan(0.5)\approx26.57^{\circ} \) east of north).

Answer:

1.875 hours

Question 10