2-D motion with constant velocity
By Matt Vonk University of Wisconsin River Falls
Background on Vectors: Some
physical quantities can be totally
described by their magnitude.
These quantities are called scalars
and include mass, time, speed, and
temperature. Other quantities
require information about their
direction to fully describe them,
they are known as vectors and
include velocity, acceleration, and
force. If I told you I kicked (exerted
a force on) a soccer ball, you might
wonder how hard I kicked it, and in
which direction. But if I told you I
warmed up my car, you wouldn’t
ask me “In which direction did you
warm up your car?” So force is a
vector quantity, but temperature isn’t.
When dealing with vector quantities, there are many times when it is helpful to separate what is happening on each axis
(the X and Y axes in this case). In this class will use this technique to simplify projectile motion, friction, and rotation
problems. At other times it will be useful to know the total magnitude of the vector (Kinetic energy depends on the
magnitude of the vector for example) or the direction of the vector. Carefully watch the 2-D motion with constant
velocity video.
For the next two questions ONLY use the grid, not the proctor.
1. Measure the velocity of the puck in the X direction (left to right) & Y direction (bottom to top).
2. Use those values to calculate the total velocity of the puck and the direction of its motion.
For the next two questions ONLY use the protractor, not the grid.
3. Measure of total velocity of the puck and the angle of its motion.
4. Use these values to calculate the components of the velocity in the X & Y directions. Also use these values to
calculate the x and y displacements of the puck after whatever time interval you used in question 3.
5. We can use these values to picture two triangles that represent velocity and displacement. For each triangle below
write in the values that you found using the grid.
x=_______
= __
y=_______
vy= ________
= __
vx=_______
NOTE: In some cases (like this one) the angle is the same on both triangles. However when the motion isn’t in a
straight line, then the angle of the velocity may not correspond to the angle of the total displacement. Other than
the angle (which may or may not be the same) you must NEVER mix the values between the triangles. At some point
in the semester I always have a student that puts a displacement on one leg of the triangle and a velocity on another
and then tries to calculate the length of the third side using trigonometry. That is always wrong.
6. Use the velocity and angle values from the protractor above to calculate the x and y displacements of the puck after
whatever time interval(s) you used in question 1.
Because of the uncertainties in your measurements it would be unlikely for the values you got using the protractor to
exactly agree with the values you got using the grid. However, on this video the uncertainties are relatively small and
your answers should agree to within a few percent.
7. For each of the six values above (velocityx, velocityy, velocitytotal, & angle of motion, x & y displacements) calculate
the percent difference between the value found with the grid and the value from the protractor.
Note: percent difference = difference/averagex100% = (value1–value2)/((value1+value2)/2)x100%