Question

true or false
true false the horizontal motion of a projectile is constant
true false the vertical velocity at the highest point is the maximum velocity
true false a projectile experiences downward acceleration due to gravity
true false the horizontal motion of projectile depends on the vertical motion
true false the vertical velocity of a straight projectile is increasing downward
true false a ball rolling on the table is a projectile
true false all projectiles are not affected by air resistance

Explanation:

1. The horizontal motion of a projectile is constant

In projectile motion, if we neglect air - resistance, the horizontal acceleration \(a_x = 0\). Using the equation \(v_x=v_{0x}+a_xt\), with \(a_x = 0\), we get \(v_x = v_{0x}\) (constant). So, this statement is True.

2. The vertical velocity at the highest point is the maximum velocity

At the highest point of a projectile's motion, the vertical velocity \(v_y = 0\). The vertical velocity is maximum at the initial point of projection (if we consider the upward - motion as positive). So, this statement is False.

3. A projectile experiences downward acceleration due to gravity

The only force acting on a projectile (neglecting air - resistance) is the force of gravity \(F = mg\) acting downwards. Using Newton's second law \(F = ma\), we get \(a = g\) (downward). So, this statement is True.

4. The horizontal motion of projectile depends on the vertical motion

The horizontal and vertical motions of a projectile are independent of each other. The horizontal motion is governed by \(x = v_{0x}t\) and the vertical motion by \(y=v_{0y}t-\frac{1}{2}gt^{2}\). There is no common variable (except time \(t\), but time is just a parameter, not a cause - effect relation between \(x\) and \(y\) motion in terms of dependence). So, this statement is False.

5. The vertical velocity of a straight projectile is increasing downward

Using the equation \(v_y=v_{0y}-gt\) (taking upward as positive). As the projectile moves down (\(t\) increases for the downward part of the motion), \(v_y\) (if we consider the magnitude) is increasing because \(v_y\) (in the downward direction) can be written as \(v_y = v_{0y}-gt\) (for the full motion, when \(t>\frac{v_{0y}}{g}\), \(v_y\) is negative and its magnitude \(|v_y|=gt - v_{0y}\) which is increasing with \(t\)). So, this statement is True.

6. A ball rolling on the table is a projectile

A projectile is an object that is given an initial velocity and then follows a path under the influence of gravity alone. A ball rolling on a table has a normal force acting on it (counteracting gravity in the vertical direction) and is not in free - fall. So, this statement is False.

7. All projectiles are not affected by air resistance

In reality, air resistance affects projectiles. The assumption of no - air resistance is a simplification for theoretical analysis. So, this statement is False.

Answer:

1. True
2. False
3. True
4. False
5. True
6. False
7. False