Legend 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.
To estimate the speed of the apple when it struck Newton, we need to consider a few factors and make some assumptions.
First, let’s assume that Newton was standing under an apple tree when the apple fell and hit him on the head. Since he was not seriously injured, it suggests that the apple's speed was not very high, and it was unlikely to cause any significant harm.
To get a rough estimate of the speed, we can use the concept of free fall and Newton's laws of motion. The apple would have fallen from a height determined by the tree branch it was hanging from. Let's assume it fell from a height of about 5 meters (16 feet).
Next, we need to consider the time it took for the apple to fall. We know that, near the surface of the Earth, the acceleration due to gravity is approximately 9.8 meters per second squared (32 feet per second squared). Using this information, we can calculate the time it would take for the apple to fall from a height of 5 meters using the equation:
Distance = (1/2) * acceleration * time^2
5 = (1/2) * 9.8 * time^2
Solving for time, we find:
time^2 = (5 * 2) / 9.8
time ≈ √(10/9.8) ≈ 1 second
Therefore, it took approximately 1 second for the apple to fall from a height of 5 meters.
Finally, we can estimate the speed of the apple just before it struck Newton by using the equation:
Speed = acceleration * time
Speed = 9.8 * 1 ≈ 9.8 meters per second
So, based on these assumptions, we estimate that the speed of the apple when it struck Newton was approximately 9.8 meters per second (22 miles per hour). However, please note that this is a simplified estimation and the actual speed might have been higher or lower depending on various factors.