Understanding the Concepts
* Projectile Motion: An object moving under the influence of gravity alone is in projectile motion.
* Initial Velocity: The velocity at which the object is launched.
* Height: The maximum vertical distance the object reaches.
* Gravity: A constant acceleration acting downwards (approximately 9.8 m/s²)
Applying the Concepts
1. Kinematic Equation: We can use the following kinematic equation to relate the initial velocity, final velocity, acceleration, and displacement (height):
v² = u² + 2as
Where:
* v = final velocity (0 m/s at the highest point)
* u = initial velocity
* a = acceleration due to gravity (-9.8 m/s²)
* s = displacement (height, h)
2. First Scenario (Initial Velocity v):
* v = 0 (at the highest point)
* u = v
* a = -9.8 m/s²
* s = h
Plugging these values into the equation:
0² = v² + 2(-9.8)h
h = v² / (2 * 9.8)
3. Second Scenario (Initial Velocity 2v):
* v = 0 (at the highest point)
* u = 2v
* a = -9.8 m/s²
* s = h' (the new height)
Plugging these values into the equation:
0² = (2v)² + 2(-9.8)h'
h' = (4v²) / (2 * 9.8)
4. Comparing Heights:
* Notice that h' = 4h
Conclusion
If the initial velocity is doubled (from v to 2v), the maximum height attained by the object will be four times the original height (h).
