Solving Vectors Algebraically

Question 1:

A football player runs directly down the field for 35 m before turning to the right at an
angle of 25° from his original direction and running an additional 15 m before getting
tackled. What is the magnitude and direction of the runner’s total displacement?

Answer: 49 m at -7.4 degrees

Question 2:

A plane travels 2.5 km at an angle of 35° to the ground, then changes direction and
travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of
the plane’s total displacement?

Answer: 7.7 km at 26 degrees

Question 3:

During a rodeo, a clown runs 8.0 m north, turns 35° east of north, and runs 3.5 m.
Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to
exit the arena. What is the clown’s total displacement?

Answer: 12.7 m at 51.8 degrees

Question 4:

An airplane flying parallel to the ground undergoes two consecutive displacements.
The first is 75 km 30.0° west of north, and the second is 155 km 60.0° east of north. What is the total displacement of the airplane?

Answer: 115 km at 57 degrees