The Question is from NEET guide , and it was created by the author Mr. S M HUSSAIN

Question

A ball is thrown at an angle of 30 degrees with the horizontal. At what point in its trajectory is the vertical component of its velocity zero?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Projectile motion
 **Related Topics**: Kinematics, vectors, velocity components
 **Prerequisites**: Understanding of projectile motion, vertical and horizontal velocity components.
## SOLUTION PATHWAY
**Given Information**:
  The ball is thrown at an angle of 30 degrees with the horizontal.
  We need to find the point where the vertical component of velocity is zero.
**Method & Steps**:
 1. Analyze projectile motion:
  Reasoning: A projectile's motion can be broken down into independent horizontal and vertical components.  Gravity only affects the vertical component, causing it to decelerate upwards and accelerate downwards.
  Formula/Rule:  The vertical velocity ($v_y$) at any time (t) is given by: $v_y = v_{0y} - gt$, where $v_{0y}$ is the initial vertical velocity, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is time.
 2. Determine the point of zero vertical velocity:
  Working: The vertical velocity is zero ($v_y = 0$) at the highest point of the trajectory.  At this point, the ball momentarily stops before beginning its downward motion.
  Key Point: The horizontal velocity remains constant throughout the projectile's flight, ignoring air resistance.
 3. Final step:
  Result: The vertical component of the velocity is zero at the highest point of its trajectory.
  Verification: This aligns with the understanding of projectile motion and the effect of gravity.
 ## OPTION ANALYSIS
A ✓: At the highest point of its trajectory: This is correct. The vertical velocity becomes zero at the apex of the parabolic path due to gravity.
B :x: Just after being thrown: The vertical velocity is maximum (but not zero) just after being thrown.  It's only zero at the highest point.
C :x: Just before hitting the ground: Just before hitting the ground, the vertical velocity is downwards and has a magnitude equal to the initial vertical velocity (but negative).
D :x: At half the maximum height: The vertical velocity is not zero at half the maximum height; it's only zero at the peak.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing horizontal and vertical components: Remember that gravity only affects the vertical component.
  How to avoid: Clearly separate the horizontal and vertical components of velocity and acceleration.
  2.Ignoring the effect of gravity: Gravity is the reason the vertical velocity changes.
  How to avoid: Always include the acceleration due to gravity (g) in your calculations for the vertical component.
 **Quick Tips**:
  1.At the highest point, the vertical velocity is always zero in projectile motion (ignoring air resistance).
  2.Visualize the parabolic path of the projectile to understand the velocity changes.

Mr. S M HUSSAIN · Answer

The correct Option is "At the highest point of its trajectory"

Mr. S M HUSSAIN · Answer

Just after being thrown

Mr. S M HUSSAIN · Answer

Just before hitting the ground

Mr. S M HUSSAIN · Answer

At half the maximum height

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