The Question is from neet-physics motion-in-a-straight-line , and it was created by the author VENKATESWARARAO

Question

Two balls are projected horizontally from the same height with different initial speeds. Neglecting air resistance, which statement is true about their times of flight?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
	**Primary Concept**: Projectile Motion
	**Related Topics**: Kinematics, Gravity
	**Prerequisites**: Understanding of vertical and horizontal motion in projectile motion
## SOLUTION PATHWAY
**Given Information**:
	* Two balls projected horizontally
	* Same initial height
	* Different initial horizontal speeds
	* Neglecting air resistance
**Method & Steps**:
	1.  Analyze the vertical motion:
		Reasoning: The time of flight for a projectile is determined solely by its initial vertical velocity and the acceleration due to gravity. Since both balls are projected horizontally, their initial vertical velocity is zero.
		Formula/Rule:  Vertical displacement:  $Δy = v_{0y}t + \frac{1}{2}gt^2$
	2. Calculate the time of flight:
		Working: Since the initial vertical velocity ($v_{0y}$) is zero for both balls and they fall from the same height ($Δy$), the time of flight (t) is dependent only on the acceleration due to gravity (g), which is constant for both. Therefore $Δy = \frac{1}{2}gt^2$ or $t = \sqrt{\frac{2Δy}{g}}$
		Key Point:  Horizontal velocity does not affect the time of flight. 
	3. Final Conclusion:
		Result:  Both balls will land at the same time.
		Verification: The time of flight is solely determined by the vertical motion and since both balls have the same initial vertical conditions, they take the same time to hit the ground. 
 ## OPTION ANALYSIS
[A] :x: The horizontal speed does not affect the time of flight; it only influences the horizontal distance traveled.
[B] :x: The horizontal speed does not affect the time of flight.
[C] ✓: This is correct as explained in the solution pathway.
[D] :x: The mass of the balls does not affect their time of flight when air resistance is neglected. 
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Assuming horizontal speed affects time of flight: This is a common mistake. Remember that horizontal and vertical motions are independent.
		2.[Error 2]: Forgetting to consider initial vertical velocity: Ensure you correctly determine initial vertical velocity, which is zero in this case. 
	**Quick Tips**:
		1.[Helpful shortcut]: The time of flight depends only on the vertical motion.
		2.[Memory aid]: Think of dropping a ball straight down and throwing a ball horizontally; both will hit the ground at the same time if released from the same height.

VENKATESWARARAO · Answer

The ball with the higher initial speed will land first.

VENKATESWARARAO · Answer

The ball with the lower initial speed will land first.

VENKATESWARARAO · Answer

The correct Option is "Both balls will land at the same time."

VENKATESWARARAO · Answer

The time of flight depends on the mass of the balls.

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