Legned has it that Isacc Newton was hit on the head by a falling apple, thus triggering his thoughts on gravity. Assuming the story is to be true, estimate the speed of the apple when it struck Newton.
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To estimate the speed of the apple when it struck Newton, we can use some basic physics principles. First, let's assume that the apple fell from a tree at a height of h meters and took t seconds to hit Newton's head.
The acceleration due to gravity near the surface of the Earth is approximately 9.8 m/s². We can use the equation s = ut + 0.5at² to calculate the distance the apple fell.
Since the apple was initially at rest, its initial velocity (u) is 0 m/s. Therefore, s = 0.5at².
Since the apple fell from a height h, the distance it fell (s) is equal to h. Therefore, h = 0.5at².
Rearranging the equation, we get t² = 2h/a.
We can now substitute the values to estimate the speed of the apple:
1. Determine the height h from which the apple fell. This would require specific information or assumptions about the height of the tree or apple branch.
2. Calculate t² using the equation t² = 2h/a, where a is the acceleration due to gravity (approximately 9.8 m/s²).
3. Take the square root of t² to find t, the time it took for the apple to fall.
4. Finally, calculate the speed v of the apple using the equation v = at, where a is the acceleration due to gravity.
Note: Without specific information about the height, it is not possible to provide an accurate estimate of the speed of the apple when it struck Newton. The story of the falling apple and Newton's realization about gravity is more of a historical anecdote rather than a precise scientific event.