Aug20
If you dive from a 3 ft diving block and enter the water at 4 ft from the base of the wall. How far do you?
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jump altogether? The answer I got is 5 ft based on Pythagorean theorm a^2+b^2=c^2. But… what is someone else dives at the same angle and enters the water 6 ft. from the base of the wall. How high would their diving block be? It can’t be the same height to maintain the same angle. How do I figure this out?
Tags: pythagorean theorm
Posted by Chunky Flik under Diving | Permalink
One does not dive in a straight line, unless one is diving straight down. The effect of gravity causes the body to accelerate in the vertical direction, while (ignoring wind resistance and the curvature of the earth) one travels at a constant speed in the horizontal direction.
So this become a question of the length of the parabolic curve that you follow in travelling from the diving block to the water. This will be slightly greater than the 5-foot straight-line distance to the landing point (the splash point).
If you are studying calculus, write an expression for the path that the body follows, and apply the following formula:
distance = Integral (sqrt(1 + (dy/dx)^2) dx)
Regarding your followup question:
If you’re assuming that everything is a straight line, you just ratio everything up (using the concept of similar triangles), so the answer is 6/5 of 3 feet.
If you’re using calculus, you need to use the concepts in the explanation above, and eventually use algebra to solve for the height of the platform.