In a lab experiment, a ball is rolled down a ramp so that it leaves the edge of the tabl – [Free] B19
In a lab experiment, a ball is rolled down a ramp so that it leaves the edge of the table horizontally at speed π£ v, as shown. It then falls a vertical distance β h to the floor and lands a horizontal distance π₯ x away from the base of the table. Air resistance is negligible. Which expression gives the speed π£ v of the ball as it leaves the ramp?
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Answer
Projectile Motion: How Far Does a Ball Travel Horizontally?
π Concept Overview
A ball rolls off a table horizontally with initial velocity v and falls from height h. With no air resistance, its motion can be analyzed in two independent parts:
- Horizontal Motion: Uniform (constant velocity)
- Vertical Motion: Accelerated (due to gravity)
π Step 1: Vertical Motion (Time to Fall)
Using the equation for vertical displacement:
y = (1/2)gtΒ²
Rearranging to find time t:
t = β(2h / g)
π Step 2: Horizontal Motion (Distance Traveled)
Horizontal distance is calculated using:
x = v Γ t
Substitute the value of t:
x = v Γ β(2h / g)
π Unit Analysis
vin m/shin mgin m/sΒ²
Units for t = β(2h/g) result in seconds, so:
x = m/s Γ s = m β Correct units for distance
β Why Other Options Are Incorrect
- Option A: 2vh/g β Units mismatch and wrong formula
- Option B: 2vΒ²/g β Doesnβt relate to height
- Option C: βNoneβ β Incorrect as one is valid
- Option E: 2h/g β Represents time squared, not distance
β Final Answer
x = v Γ β(2h / g)
This is the correct horizontal distance the ball travels from the edge of the table.