All Solutions
Page 55: Standardized Test Practice
**A** states that to solve any physics problem we need to draw a vector diagram first.
This is incorrect, there are many problems concerning only vector intensities and scalar quantities where vector diagrams are not needed.
So statement **A** is false.
**B** states that the length of a vector should be proportional to the data.
The drawn length of a vector must adequately represent the vector’s intensity. To accomplish this, the data describing the vector must be considered.
So statement **B** is true.
**C** states that vectors can be added by simply adding their intensities(their lengths).
This is very incorrect, the fact that vectors cannot be added by just adding their intensities is, in a sense, what makes them vectors and not scalars.
Their direction has to be considered, and figures in the calculation.
So statement **C** is false.
**D** states that vectors can be added in either triangles or straight lines.
The statement is quite simply true.
When adding vectors, they can be drawn on the same straight line if they are parallel(or antiparallel) but must be drawn in a triangle if they point in different directions.
So statement **D** is true.
Statements **A** and **C** are false.
Statements **B** and **D** are true.
The cyclist was increasing his displacement (moving away from initial position) up to then.
At C, the velocity becomes negative, meaning that the cyclist turns around,
and in doing so, decreases his displacement as he heads back to initial position.
Answer: C
So it is the farthest from inital point.
II, IV, III, I
(Section III and section I are very close, but section I seems to have a larger change in position on the graph)
(the squirrel returns to initial height)
the rat displaces first 1.0m to the north, then later, 0.8m to the south.
Vertical component: 0.2m north.
Total horizontal displacement: 0.7 m east.
0.7m east, 0.2m north.
By placing the origin of a coordinate system at the initial point, (+x) being East, (+y) north, this position would represent the point with coordinates (0.7,0.2)m.
Its distance from the origin is calculated with the Pythagorean theorem:
$$
d=sqrt{0.7^2+0.2^2}=0.73m=73cm
$$