PreAP Physics Vector Addition Practice
Converting Cartesian to Polar
(like the river & boat problem from class below)
1. A boat that can drive at a max speed of 10 m/s tries to cross a river to the North that flows East
at 5 m/s. Find the resultant velocity (magnitude and direction) of the boat in the river.
2. Add the following vectors 3 m/s x + 6 m/s y. Sketch a picture to show the addition of the
vectors. Express your answer as a polar vector.
3. Add the following vectors -43 m x + 64 m y. Sketch a picture to show the addition of the
vectors. Express your answer as a polar vector.
4. Two hockey sticks push against a puck. The first stick pushes 14 Newtons in the negative ydirection, while the second pushes 26 Newtons in the negative x-direction. Find the resultant
force on the puck. Write your solution in Cartesian form and then in polar form.
Converting Polar to Cartesian
(like the baseball problem from class below)
1. A baseball is hit with an initial velocity of 63 m/s at 27 degrees above the ground. Find the
horizontal and vertical components of the velocity.
2. A sailboat makes a course that takes it 238 km in a direction 64 degrees North of East from
Miami. Find the Cartesian coordinates of its location relative to Miami.
3. The Lunar Module comes to rest on the moon. As it descends it has a velocity of 10 m/s along a
line 15 degrees from the vertical (let’s arbitrarily call it 15 degrees E of S in the coordinate
plane). Find the horizontal and vertical components of this velocity.
Adding multiple vectors
1. A family takes a road trip. They drive at 27 m/s at 26 degree N of E. Then they drive at 24 m/s
at 72 degrees N of W. Then they drive along a dirt road at 12 m/s at 40 degrees S of W. What
was the total velocity during the entire trip. Remember velocity is a vector.
2. Extension: If the whole trip took 3 hours and 23 minutes, what was the displacement of the
family? Recall that displacement is a vector, and remember its relationship to velocity (use an
equation…)
3. Six forces act on an object. Find the net force.
a. 12 N x
b. 16 N x + 7 N y
c. 32 N @ 43 degrees N of W
d. 8 N @ 72 degrees S of W
e. 22 N @ 12 degrees E of S
f. -14 N y