Question

extra practice
q1. looking at the following graph, which of the following statements are correct?
(select all that apply)
a. the overall magnitude of the velocity decreases as the object approaches the maximum vertical displacement.
b. the overall magnitude of the velocity decreases to zero as the object approaches the maximum vertical displacement.
c. the angle of the trajectory, to the horizontal, decreases to zero as the object reaches the highest point of the parabola.
d. the horizontal component of velocity changes as the vertical height of the projectile changes.
e. the minimum velocity which a projectile can have is given by $v_{0x}$.

Explanation:

Step1: Analyze velocity at max - height

In projectile motion, the vertical component of velocity \(v_y\) decreases as the object approaches the maximum vertical displacement. The overall velocity magnitude \(v = \sqrt{v_x^2 + v_y^2}\). Since \(v_x\) is constant (in the absence of air - resistance) and \(v_y\) decreases, the overall magnitude of the velocity decreases as the object approaches the maximum vertical displacement. So, statement a is correct.

Step2: Consider velocity at max - height

At the maximum vertical displacement, the vertical component of velocity \(v_y=0\), but the horizontal component \(v_x
eq0\). So the overall magnitude of the velocity does not decrease to zero, and statement b is incorrect.

Step3: Analyze the angle of the trajectory

The angle of the trajectory \(\theta=\tan^{- 1}(\frac{v_y}{v_x})\). At the highest point of the parabola, \(v_y = 0\), so \(\theta = 0\). Thus, the angle of the trajectory to the horizontal decreases to zero as the object reaches the highest point of the parabola, and statement c is correct.

Step4: Consider the horizontal component of velocity

In the absence of air - resistance, the horizontal component of velocity \(v_x\) is constant throughout the motion of the projectile and does not change as the vertical height changes. So, statement d is incorrect.

Step5: Analyze the minimum velocity

The minimum velocity of a projectile occurs at the maximum height. At this point, \(v_y = 0\), and the velocity is equal to the horizontal component of velocity \(v = v_x\). So the minimum velocity which a projectile can have is given by \(v_{0x}\) (assuming no air - resistance and initial horizontal velocity \(v_{0x}\)), and statement e is correct.

Answer:

A. The overall magnitude of the velocity decreases as the object approaches the maximum vertical displacement.
C. The angle of the trajectory, to the horizontal, decreases to zero as the object reaches the highest point of the parabola.
E. The minimum velocity which a projectile can have is given by \(v_{0x}\).