laqitta asked in Science & MathematicsMathematics · 1 decade ago

# I know this is easy!?

My brain is on off today. Diving from a 3 foot high diving block, you enter the water 4 feet from the base of the wall. How far did you jump altogether?

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• 1 decade ago

If you are simply asking what is the straight line distance from the endge of the diving block to your point of impact on the water's surface, then the answer can easily be found using the Pythagorean Theorem:

d^2 = 3^2 + 4^2 = 25

d = 5 feet

If instead you are asking what is the total distance that you've travelled in the arc you created when you jumped from the diving block and into the water, then it gets to be more fun and interesting. ^.^

There is no unique answer without knowing additional things, such as how high you jumped, or how fast you were moving forward. We can, however, find the greatest and least distances that are theoretically possible.

If you were allowed to touch the front of the diving block, then the theoretical minimum is a straight line of 5 feet. This assumes that you pushed yourself at exactly a 36.87-degree angle of depression and with enough force that you made practically a straight line right into the water.

If you were not allowed to push yourself off, that is, you only either jumped off the top or ran forward and dropped off, then the problem is a bit more complex. Your maximum trajectory has no upper bound, and is practically limited only by your weight and the strength of your leg muscles.

For a minimum trajectory, you must have zero upward motion (i.e. you cannot have jumped off), or you will need to spend extra time moving upward and downward just to get back to the same level as the diving block. So, you need to run straight forward and drop off the block, and at the exact speed which will place you exactly 4 feet from the block by the time you hit the water. Finding the exact distance travelled would require a bit of calculus, unfortunately. However, we can still calculate both the speed at which you need to be running forward, and the time it will take before you actually hit the water, using simple algebra.

Since the acceleration due to gravity is constant at 32f/s^2, you can find the time it would take to drop the 3 feet using the formula y=1/2(g)(t^2) where y=3 feet and g=32ft/s^2, so to solve for t:

t^2 = 2y/32 = y/16

t = sqrt(y)/4 = sqrt(3)/4 ~= 0.433 seconds

Less than half a second to fall. So how fast do you need to be moving forward to cover 4 feet in 0.433 seconds? Use the distance formula, d=r*t, where d=4 feet and t=0.433 seconds, so to solve for r:

r = d/t = 4/0.433 ~= 9.24 feet per second

...or about 6.3 miles per hour, a fair running speed.

• 1 decade ago

I'm guessing this is related to homework, so be warned that this is one of those cases where the teacher's answer (on the middle or high school levels) may be an oversimplification.

If you are studying simple geometry your teacher is probably looking for you to use the Pythagorean Theorem (a^2 + b^2 = c^2) to find the length of the line from your point of departure (0,3) to your point of entry into the water (4,0).

That answer, unfortunately, would also be incorrect if the question is "what is the length of the path you traveled during your jump?" because you don't travel in a straight line from start to finish. Instead, your trajectory is a parabola. There are literally an INFINITE number of possible trajectories. Jumping straight out is the shortest of these. The higher upwards you jump at the start, the farther you travel before hitting the water (even though you hit the same point). To illustrate, try throwing something in a trash can. You can throw with a little arc or with a very high arc and still hit the trash can (you're just adjusting the initial horizontal velocity to compensate).

Hopefully you just need to know how far it is from your starting point to the finish and can rely on Pythagoras. Otherwise you need to set up some scenarios and do a some more serious calculations with a bit of calculus thrown in to determine the path length.

• 1 decade ago

Your displacement from one point to the other is what you have already been told and the straight line distance would be 5 feet.

If you wanted to determine the distance travelled along the parabolic path, you would have to know how fast you can jump to get an initial velocity. Then, you will find out that there are going to be two initial angles that will work, one shallow and one steep.

This would lead you to the equation of a parabola. Then you would have to take the line intergral of the parabola between the two known points.

I seriously doubt that this is the question you are really asking, but it would be fun to do it.

• 1 decade ago

The answer is 4 feet, but not that easy.

You can jump only in one direction upward or horizontal so in horizontal direction you have jumped only four feet.

If the question however was how much you have traveled in the air before hitting the water then using Pythagorean theorem it should be 5 feet.

Don't feel bad. It is a tricky question.

• Larry
Lv 6

You are describing a triangle that is 3 feet tall and 4 feet base, and it is a right angle triangle. So you use the Pythagorean theorem to get that the hypotenuse is the square root of 3 squared plus 4 squared, or in other words, 5.

• wdmc
Lv 4

Well...the answer is either 5 feet or impossible to determine.

5 feet is just the answer you get from using the Pythagorean theorem.

But people hardly ever jump in a straight line, in which case this would be a projectile motion problem. If it is one of these, it is impossible to answer because you don't know the initial angle or the initial force of the jump.

• 1 decade ago

If you somehow jumped in exactly a straight line it would be 5 feet. In real life you could not possibly dive in an exact straight line, so the curve would be more than 5 feet.

• 1 decade ago

assuming you actually jumped ever from the edge of the wall, it would be 3 squared + 4 squared = 25...take square root and it is 5

pythagorian theorem...

• 1 decade ago

hi there

i suppose 7 feet

it probably sounds stupid but dats d most practical ans i can make out of dis ques.

cya

dee

Source(s): elementary mathematics
• Anonymous

dont know 7
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