An object is thrown vertically upward with a velocity u. The greatest height h to which it will rise before falling back is given by
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Maximum height = u² / 2g
Explanation:
Equation for motion for a vertically ascending body
v² - u² = - 2gh (Negative sign for "2gh" because the body is moving opposite to "g" i.e. acceleration due to gravity which always acts downwards)
v = 0 (as the body will stop for a fraction of time when it reaches the top)
- u² = - 2gh
u² = 2gh (negative sign will get cancelled because it is on both sides)
u² / 2g = h
Hence, the maximum height which the object can reach will be u² / 2g
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