(30 points)
true/false (5 questions, 10 points)
_____1. a quantity that has only magnitude is called a vector.
_____2. the vector sum is called the resultant.
_____3. the length of a vector represents its magnitude.
_____4. the horizontal acceleration of a ball in flight is -10 $\frac{m}{s^2}$ due to the effects
_____5. a ball will travel the farthest if thrown almost horizontally.
multiple-choice (10 questions, 20 points). circle the best answer.
_____6. what is the resultant of a 3-unit vector and a 4-unit vector at right angles
a. 5 units
b. 6 units
c. 7 units
d. 9 units
(with a right triangle diagram labeled r, 3, 4)
_____7. which of the following would not be considered a projectile?
a. a cannonball thrown straight up.
b. a cannonball rolling down a slope.
c. a cannonball rolling off the edge of a table.
d. a cannonball thrown through the air.
_____8. in the absence of air resistance, the angle at which a thrown ball will go the
a. 15°
b. 30°
c. 45°
d. 60°
_____9. a cannonball is launched from the ground at an angle of 30 degrees above

Question

(30 points)
true/false (5 questions, 10 points)
_____1.  a quantity that has only magnitude is called a vector.
_____2.  the vector sum is called the resultant.
_____3.  the length of a vector represents its magnitude.
_____4.  the horizontal acceleration of a ball in flight is -10 $\frac{m}{s^2}$ due to the effects
_____5.  a ball will travel the farthest if thrown almost horizontally.
multiple-choice (10 questions, 20 points). circle the best answer.
_____6.  what is the resultant of a 3-unit vector and a 4-unit vector at right angles
        a.  5 units
        b.  6 units
        c.  7 units
        d.  9 units
        (with a right triangle diagram labeled r, 3, 4)
_____7.  which of the following would not be considered a projectile?
        a.  a cannonball thrown straight up.
        b.  a cannonball rolling down a slope.
        c.  a cannonball rolling off the edge of a table.
        d.  a cannonball thrown through the air.
_____8.  in the absence of air resistance, the angle at which a thrown ball will go the
        a.  15°
        b.  30°
        c.  45°
        d.  60°
_____9.  a cannonball is launched from the ground at an angle of 30 degrees above

Accepted Answer

### Question 1 (True/False)
# Explanation:
## Step1: Recall vector definition
A vector has both magnitude and direction; a scalar has only magnitude.
## Step2: Evaluate the statement
The statement says a quantity with only magnitude is a vector, which is wrong.
# Answer: False

### Question 2 (True/False)
# Explanation:
## Step1: Recall resultant definition
The vector sum of two or more vectors is called the resultant vector (or resultant).
## Step2: Evaluate the statement
The statement matches the definition.
# Answer: True

### Question 3 (True/False)
# Explanation:
## Step1: Recall vector magnitude representation
In a vector diagram, the length of the vector arrow represents its magnitude (scaled appropriately).
## Step2: Evaluate the statement
The statement is correct.
# Answer: True

### Question 4 (True/False)
# Explanation:
## Step1: Recall projectile motion horizontal acceleration
In projectile motion, horizontal acceleration is $ 0 \, \text{m/s}^2 $ (no air resistance), and vertical acceleration is $ -g \approx -10 \, \text{m/s}^2 $.
## Step2: Evaluate the statement
The statement incorrectly attributes $ -10 \, \text{m/s}^2 $ to horizontal acceleration.
# Answer: False

### Question 5 (True/False)
# Explanation:
## Step1: Recall projectile range formula
The range $ R = \frac{v_0^2 \sin(2\theta)}{g} $. Maximum range occurs at $ \theta = 45^\circ $; lower angles (near horizontal) give shorter range than $ 45^\circ $.
## Step2: Evaluate the statement
The statement is wrong (max range at $ 45^\circ $, not near horizontal).
# Answer: False

### Question 6 (Multiple - Choice)
# Explanation:
## Step1: Apply Pythagorean theorem
For two vectors at right angles, the magnitude of the resultant $ R $ is $ R=\sqrt{A^{2}+B^{2}} $, where $ A = 3 $, $ B = 4 $.
## Step2: Calculate resultant
$ R=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 $ units.
# Answer: a. 5 units

### Question 7 (Multiple - Choice)
# Explanation:
## Step1: Recall projectile definition
A projectile is an object moving under gravity (and air resistance, if considered) with an initial velocity, and no other continuous horizontal force.
## Step2: Analyze options
- Option a: Cannonball thrown straight up is a projectile (gravity acts).
- Option b: Cannonball rolling down a slope has a slope - related force (not just gravity as a projectile; it's a sliding object on a slope, not a projectile).
- Option c: Cannonball rolling off a table is a projectile (falls under gravity after leaving the table).
- Option d: Cannonball thrown through the air is a projectile.
# Answer: b. A cannonball rolling down a slope.

### Question 8 (Multiple - Choice)
# Explanation:
## Step1: Recall projectile range formula
The range of a projectile $ R=\frac{v_0^{2}\sin(2\theta)}{g} $. The maximum value of $ \sin(2\theta) $ is 1, which occurs when $ 2\theta = 90^{\circ}$, so $ \theta = 45^{\circ} $.
## Step2: Evaluate options
Among the given options, $ 45^{\circ} $ (option c) gives the maximum range (since $ \sin(90^{\circ}) = 1 $, and for other angles like $ 15^{\circ},\ 30^{\circ},\ 60^{\circ} $, $ \sin(2\theta) $ is less than 1).
# Answer: c. $ 45^{\circ} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1 (True/False)

Step1: Recall vector definition

Step2: Evaluate the statement

Step1: Recall resultant definition

Step2: Evaluate the statement

Step1: Recall vector magnitude representation

Step2: Evaluate the statement

Answer:

Question 2 (True/False)