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[Phys-L] student difficulties with velocity as a vector?



The other day, I gave the following problem in class (1st semester of
algebra-based physics for mostly junior life-science majors; pre-calc
prerequisite):

A ball rolls off a horizontal table with a speed of 2 m/s. If we start
a timer at the exact moment the ball leaves the table, we find it takes
0.5 seconds to hit the floor.

I then asked a series of questions:

1. What is the ball's initial speed (i.e., the speed when the timer was
started)?
A. 2 m/s [78%]
B. Greater than 2.5 m/s [9%]
C. Less than 1.5 m/s [13%]

2. What is the ball's initial horizontal velocity?
A. 2 m/s [96%]
B. Greater than 2.5 m/s [0%]
C. Less than 1.5 m/s [4%]

3. What is the ball's initial vertical velocity?
A. 2 m/s [29%]
B. Greater than 2.5 m/s [21%]
C. Less than 1.5 m/s [50%]

My question to the list is: how do you explain the poor performance on
question #3? By the way, each question was asked during class and
students respond via remotes. After each question, I go over the answer
to the question. Students have been working with vectors for a while
now, can add/subtract vectors and can break them into components when
they need to. They know that during the ball's flight we can assume the
gravitational force is the only force acting and, in that case, the
ball's acceleration is 9.8 m/s2 downward.

By the way, I followed this up with these questions:

4. What is the change in the ball's horizontal velocity during the 0.5
seconds?
A. 2 m/s [0%]
B. Greater than 2.5 m/s [22%]
C. Less than 1.5 m/s [78%]

5. What is the change in the ball's vertical velocity during the 0.5
seconds?
A. 2 m/s [4%]
B. Greater than 2.5 m/s [78%]
C. Less than 1.5 m/s [17%]

6. What is the ball's final horizontal velocity?
A. 2 m/s [39%]
B. Greater than 2.5 m/s [4%]
C. Less than 1.5 m/s [57%]

7. What is the ball's final vertical velocity?
A. 2 m/s [0%]
B. Greater than 2.5 m/s [100%]
C. Less than 1.5 m/s [0%]

Again, I discuss each answer before moving on to the next question (and
answer any questions students may ask about the question). Notice how
most students realize the ball's horizontal velocity doesn't change (see
#4) yet most still think that the ball's final horizontal velocity must
be small since the ball is going "more down than over".

____________________________________________________
Robert Cohen, Chair, Department of Physics
East Stroudsburg University; E. Stroudsburg, PA 18301
570-422-3428; www.esu.edu/~bbq