# Worksheet: Using Vectors to Solve Real-World Problems

Q1:

An airplane is heading north at an airspeed of 600 km/h, but there is a wind blowing from the southwest at 80 km/h. How many degrees off course will the plane end up flying, and what is the plane’s speed relative to the ground? Give your answers correct to one decimal place.

• A , 684.7 km/h
• B , 659.0 km/h
• C , 684.7 km/h
• D , 659.0 km/h
• E , 680.0 km/h

Q2:

A river is one half mile wide with a current flowing at 2 miles per hour from east to west. A man can swim at 3 miles per hour in still water. He stands on the south bank, so how many degrees east of north should he head at this rate in order to travel directly north across the river? Give your answer correct to one decimal place. What would the answer to this problem be if the river flowed at 3 miles per hour and the man could swim only at the rate of 2 miles per hour?

• A ,
• B , it is not possible for him to head directly north in the second case.
• C ,
• D , it is not possible for him to head directly north in the second case.
• E , it is not possible for him to head directly north in the second case.

Q3:

A woman leaves home and walks 3 miles west and then 2 miles southwest. How far from home is she? In what direction must she walk to directly head home? Give the distance, in miles, correct to two decimal places and the direction, in degrees, to one decimal place.

• A 4.15 miles, north of east
• B 21.50 miles, north of east
• C 4.15 miles, north of east
• D 4.64 miles, north of east
• E 4.64 miles, east of north

Q4:

A man started walking from home and walked 4 miles east, 2 miles southeast, 5 miles south, 4 miles southwest, and 2 miles east. How far did he walk in total? If he walked in a straight line back home, how far would he have to walk? Give your answer correct to three decimal places if necessary.

• A 13 miles, 6.7 miles
• B 15 miles, 13.8 miles
• C 15 miles, 10.3 miles
• D 17 miles, 10.3 miles
• E 17 miles, 13.8 miles

Q5:

A plane is heading north with an airspeed of 500 km/h. However, there is a wind blowing from the southeast towards northwest at 50 km/h. How many degrees off course will the plane end up flying? What is the plane’s speed relative to the ground? Give your answers correct to one decimal place.

• A , 552.3 km/h
• B , 536.5 km/h
• C , 552.3 km/h
• D , 536.5 km/h
• E , 550.0 km/h

Q6:

A body moved 28 m due east and then 14 m due north. Determine the body’s displacement, stating its direction to the nearest minute.

• A m, north of east
• B m, north of east
• C m, north of east
• D m, north of east

Q7:

An airplane was flying due north at 150 miles per hour . A wind was pushing the airplane due east at 40 miles per hour. After 1 hour, the plane started flying east of north. Assuming the plane started at , find, in ordered pair, the position of the plane after 2 hours from starting the flight. Let north be the direction of the positive -axis and east the positive -axis.

• A
• B
• C
• D
• E

Q8:

An airplane flies at an airspeed of 500 km/h. If there is a wind blowing at 80 km/h from northwest, on what bearing must the pilot fly the plane to travel due north? Give your answer to three decimal places.

Q9:

Two points and lie on a field. James wants to fly his drone from to and measures the bearing to be . He also measures that a 10 mph wind is blowing on a bearing of . Give your answer to two decimal places.

If he is going to fly the drone at 25 mph, on what bearing would he have to fly to travel from to ?

• A
• B
• C
• D
• E

Calculate the ground speed of the remote control plane.

• A 24.71 mph
• B 12.14 mph
• C 74.15 mph
• D 20.12 mph
• E 19.89 mph