Challenging Physics Question!!!?

Question

In the 1968 Olympics in Mexico City, Bob Beamon shattered the world long jump record with a jump of 8.90m. His speed on take-off was measured at 9.5m/s, about equal to that of a sprinter. How close did he come to achieving maximum range for his speed in the absence of air resistance? The value of g (gravity) in Mexico City is 9.78m/s/s.
(Please show how you got the answer!! Best Responce gets 10 points!!)

Answer 1

Bob was travelling at 9.5 meters/sec when he started his jump. To gain maximum range he needed to jump at a perfect 45 degree angle. If he had done so, his initial velocity vertically would have been 9.5 /sqrt(2) = 6.72 meters/sec. His maximum height would occur at time t where 6.72-gt = 0.
9.78t = 6.72
t = 6.72/9.78 = 0.687 secs

After that he would fall for another 0.687 secs till he hit the ground for a total of 2(0.697) = 1.37 secs

In this time, he would have traveled (6.72)(1.37) meters horizontally or 9.23 meters.

So his jump of 8.90 meters was 0.33 meters short of perfection.

Note that air resistance (which is pretty important in reality) would have the effect of making the maximum achievable jump shorter than 9.23 meters. So his jump was better than it appeared..

Answer 2

Hey, I think that "heartsensei" did a great job answering your question.

But the question is flawed, in my view.

Indeed, with long jump, what typically happens is that the jumper arrives at a given speed, purely along the horizontal (x) axis, AND then jumps up on the board, adding a vertical component.

I would assume that the "speed" measured at 9.5 m/s was just the horizontal component, while the vertical component was not measured.

Clearly, Bob did NOT shoot up at 45 degrees, with equal speeds on the vertical and horizontal axes!

Because of this, we cannot really tell how close (or not) Bob Beamon came to the best theoretically possible jump, given the initial speed.

Answer 3

You cannot answer this question with the supplied information. The reason is that some of the energy in a long jump comes from the final step, with the foot pushing off forcefully from the ground. You have no way of knowing this contribution.

You can calculate how close he was to a perfect trajectory with no imuplsive force at takeoff from a speed of 9.5 m/s, but this is absolutely not a measure of how close he came to maximum range.

Answer 4

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