Note: Everything below was submitted by a 'student' to me as teacher by email. Comments between ----------- are entered by the student at the time he was taking the test. Comments between @@@@@@@@@ were made by me after the fact.
name: XXXX XXXX
results: This is a sample application of MyTestAssistant based on the practice problem module in Chapter 3 of http://www.prenhall.com/walkerphysics/
There are 5 problems in this demo.
This is fully functional.
Problem 1: Vector A has magnitude 76 units and direction, counterclockwise from east, of 37 degrees, what is the value of its x-component to 1 decimal place? What is its y-component?
_____________________
37
cos
0.7986355100472928*76
60.6962987635942660
60.7
{60.7}_correct
37
sin
0.6018150231520483*76
45.73794175955567
45.7
{45.7}_correct
@@@@@@@@
Note: The numbers in the problem change.
@@@@@@@@
Your grade on this problem is: 100
Problem 2: A vector has x-component -7.8 and y-component 6.9, what is its magnitude to the nearest tenth of a unit ? What is its direction to the nearest tenth of a degree?
_____________________
7.8
^2
60.839999999999996
mem->
6.9
^2
47.61000000000001
mem+
108.45
108.5
{108.5}_wrong
(Did you remember to use the sqrt function? See section 3-2 in Walker.)
The correct answer is 10.4
@@@@@@@@@@@
The student did forget the squareroot
@@@@@@@@@@@
__________
6.9/-7.8
-0.8846153846153847
atan
-41.49646835521555
-41.5
{-41.5}_wrong
(Did you use the inverse tangent function? If the result was negative you have to adjust it to the apporpriate quadrant. See section 3-2 in Walker.)
The correct answer is 138.5
@@@@@@@@@@@@
The actual vector is in the second quadrant
@@@@@@@@@@@@
__________
Your grade on this problem is: 0
Problem 2: A vector has x-component -2.1 and y-component 0.8, what is its magnitude to the nearest tenth of a unit ? What is its direction to the nearest tenth of a degree?
_____________________
--------
I rework the previous problem here.
--------
@@@@@@@@
The student does have the ability to rework a problem
@@@@@@@@
2.1
^2
4.41
mem->
.8
^2
0.6400000000000001
mem+
5.050000000000001
sqrt
2.247220505424423
2.2
{2.2}_correct
.8/-2.1
-0.38095238095238093
atan
-20.854458039578347+180
159.14554196042167
159.1
{159.1}_correct
Your grade on this problem is: 100
Problem 3: Vector A is 10 units long and is at angle of 48 degrees counterclockwise from east . Vector B is of length 10 units and is at an angle of -30 degrees. What is the direction to the nearest tenth of a degree measured counterclockwise from east of A+6.4B ? What is its magnitude to the nearest tenth of a unit?
_____________________
48
cos
0.6691306063588582*10
6.691306063588582
mem->
-30
cos
0.8660254037844387*10*6.7
58.02370205355739
mem+
--------
X component now in memory
--------
48
sin
0.7431448254773942*10-.5*10*6.7
-26.06855174522606
--------
Y component above
--------
-26.06855174522606/64.71500811714597
-0.40282080623457894
atan
-21.940601659158513+360
338.0593983408415
338.1
--------
angle below
--------
{338.1}_correct
26.06855
^2
679.5692991024999
mem->
64.715
^2
4188.031225000001
mem+
4867.6005241025
sqrt
69.76819134894138
69.8
--------
magnitude below
--------
{69.8}_wrong
(Did you use the squareroot function? See 'Adding Vectors' on page 61 in Walker.)
The correct answer is 66.8
__________
Your grade on this problem is: 50
@@@@@@@@@@
Looking above I see the student used 6.7 and should have used 6.4
@@@@@@@@@@
Problem 4: A car traveling at 14.5 m/s northwest reaches a curve and 15.8 seconds later it is heading north at 15 m/s, what is the magnitude of its average acceleration to 2 decimal places? What is the direction of the average acceleration measured counterclockwise from east to the nearest tenth of a degree?
_____________________
--------
calculating deltaVx
--------
45+90
135
cos
-0.7071067811865475*14.5
-10.253048327204938
mem->
0-1*-10.253048327204938
10.253048327204938
--------
calculating deltaVy
--------
@@@@@@@@@@@
Error Below the student should have used 135 not 131
@@@@@@@@@@@
131
sin
0.7547095802227721*14.5
10.943288913230196
mem->
15-10.943288913230196
4.056711086769804
--------
calculate magnitude
--------
4.0567
^2
16.45681489
mem->
10.253
^2
105.124009
mem+
121.58082389
sqrt
11.026369479116867
^2
121.58082388999999
mem+
243.16164778
sqrt
15.59364126110383515.59
15.59
{15.59}_wrong
--------
deltaVy/deltaVx
--------
4.0567/10.253
0.39565980688578955
atan
21.586714390574045
21.59
{21.59}_wrong
(See Active Example 3-2 on page 67 in Walker. Use the atan(Vy/Vx))
The correct answer is 24.8
__________
--------
calculate magnitude
--------
4.0567
^2
16.45681489
mem->
10.253
^2
105.124009
mem+
121.58082389
sqrt
11.026369479116867
^2
121.58082388999999
mem+
243.16164778
sqrt
15.59364126110383515.59
15.59
{15.59}_wrong
@@@@@@@@@@@@
The student forgot to divide by the time
@@@@@@@@@@@@@
(See Active Example 3-2 on page 67 in Walker.)
The correct answer is 0.72
__________
Your grade on this problem is: 0
Problem 5: A boat is traveling with a speed 4.3 mph over the water and at a direction of 48 degrees counterclockwise from east. The river itself is flowing east at 4 mph relative to its bank. What is the speed of the boat relative to the river bank to the nearest hundredth of a mph ? What is the angle of progress of the boat with respect to the river bank to the nearest tenth of a degree?
_____________________
48
cos
0.6691306063588582*4.3
2.8772616073430903+4
6.87726160734309
--------
X component above
--------
48
sin
0.7431448254773942*4.3
3.195522749552795
^2
10.211365642909454
mem->
--------
Y component squared in memory
--------
6.877
^2
47.293129
mem+
--------
X^2+Y^2 in memory and recalled below
--------
57.50449464290946
sqrt
7.5831718062371145
7.58
{7.58}_correct
--------
magnitude above
--------
10.211
6.877/10.211
@@@@@@@@@@@@
Insead of finding Vy/Vx the student calculates Vx/Vy^2 above which leads to the error below
@@@@@@@@@@@@
0.6734893742042894
atan
33.95984762876643
34
{34}_wrong
(See Exercise 3-2 on page 70 in Walker.)
The correct answer is 24.9
__________
Your grade on this problem is: 50
Your Grade for this exercise is 60