Test on Horizontal and projectile motion

Question 1: The horizontal velocity of a projectile remains constant throughout its flight when air resistance is neglected.

A. Yes

B. No

Explanation: In the absence of air resistance, there are no horizontal forces acting on the projectile. According to Newton's First Law of Motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Therefore, the horizontal velocity of the projectile remains constant throughout its flight.

Question 2: Which of the following statements accurately describes the vertical motion of a projectile, assuming air resistance is neglected?

A. The vertical velocity component remains constant throughout the flight.

B. The projectile is subject to a constant acceleration due to gravity.

C. The vertical position can be calculated using the formula y = v₀ᵧ ⋅ t - (1/2) ⋅ g ⋅ t².

D. At the maximum height, the vertical velocity component reaches its peak positive value.

Explanation: In the vertical direction, the projectile is subject to constant acceleration due to gravity, which is approximately 9.81 m/s² downwards. This means the vertical velocity changes over time, thus option 0 is incorrect. The vertical position at any time t can be found using the equation y = v₀ᵧ ⋅ t - (1/2) ⋅ g ⋅ t². At the peak of its trajectory (maximum height), the vertical velocity component momentarily becomes zero, not its peak positive value, making option 3 incorrect.

Question 3: The maximum height reached by the cannonball in the worked example is 35.0 meters.

A. Yes

B. No

Explanation: In the worked example, the maximum height (h) is calculated as 31.86 meters. The statement that the maximum height is 35.0 meters is incorrect.

Question 4: Launch angles that are complementary to each other, such as 30° and 60°, will result in the same horizontal range when launched with the same initial velocity and in the absence of air resistance.

A. Yes

B. No

Explanation: The study materials explicitly state: 'Angles complementary to each other (e.g., 30° and 60°) will result in the same range, but different maximum heights and times of flight.'

Question 5: According to the provided study materials, which of the following expressions correctly represents the total time of flight (t_f) for a projectile, assuming the launch and landing heights are the same?

A. t_f = (v₀ · sin θ) / g

B. t_f = 2 · (v₀ · sin θ) / g

C. t_f = (v₀² · sin(2θ)) / g

D. t_f = 2 · (v₀ · cos θ) / g

Explanation: The study materials state, 'The total time of flight is twice the time it takes to reach maximum height... t_f = 2 · t_h = 2 · (v₀ · sin θ) / g'. This directly matches option B. Option A is the time to reach maximum height (t_h), not the total time of flight. Option C is the formula for horizontal range (d). Option D uses the horizontal component of velocity in an incorrect way for total time of flight.