Thursday, February 25, 2010

Bowling Puzzler V: The Perfect Velocity

Ok, for all of you who are algebraically inclined, this one shouldn't be too difficult, but for those of you who aren't, good luck. You might be able to get in the right ballpark, but the exact answer will be elusive.

Most modern bowling alleys have some way of gauging the speed of a ball. I typically throw anywhere between 12 and 18 mph depending upon the shot. If you release your bowling ball directly at the foul line and it rolls to strike the center of the headpin, it will have traveled a distance of about 60 feet. If you throw your ball at a snail's pace of 1 mph, it will take approximately 40.9 seconds to cover this distance. If you throw the heater at 20 mph, it will cover the same distance in just over 2 seconds. Here's the bowling puzzler of the week:


At what velocity in the units miles per hour (mph) must you throw the ball for its speed to be exactly equal to the time in seconds that it takes for the ball to travel 60 feet?

4 comments:

  1. My answer is pi (huckleberry): 3.14

    (you know placing a problem such as this in my hands is tantamount to giving me a palette full of oil paints, a brush, and asking me to paint you a copy of the Mona Lisa)

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  2. My guess is a ball thrown at 6.4 mph would take 6.4 secs to reach the headpin. I play with a lady who bowls at that speed on Sundays. She's pretty accurate with it too lol

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  3. I got 6.4 mph (with some squirmy decimals).

    This has nothing to do with my algebra skills, and a lot to do with the fantastic new conversion program I've wasting this morning playing with.

    Now I am finally comfortable saying that four British gallons equals 1,229.773 tablespoons and 17 lux equals 1.5794 foot-candles.

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  4. MD and K-Terk are correct, but the exact answer is that a ball thrown 6.396 mph will arrive at the headpin in 6.396 seconds. Here's how the problem is solved. Time time in seconds for the ball to travel is calculated as 40.909 divided by speed in mph. So:

    Time = 40.909/speed

    We want to solve that equation for the condition when time = speed, so the equation can be rewritten as:

    speed = 40.909/speed

    or...

    speed x speed = 40.909

    So, the answer is

    speed = square root (40.909)

    speed = 6.396 mph

    Thanks for playing!

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