Fun with Fundamentals: Problem 226

June 1, 2000
The game was already out of hand for Smokin' Joe Brown of the Hooterville Mud Hens when Slim Slam stepped up to the plate

Problem 226 - Catch of the day

Ready for a major-league challenge?

The game was already out of hand for Smokin' Joe Brown of the Hooterville Mud Hens when Slim Slam stepped up to the plate, looking for his fourth hit of the night. Brown aimed his first pitch at the batter's ankle to back him off the plate, but Slim was ready and golfed it directly over Brown's shoulder into straight-away center. The ball looked as if it would drop in, but the centerfielder, who was only 50 m from home plate, made a spectacular ankle-high catch. How fast was he running and did he have to come in or go out to make the play?

Ball trajectory
Initial speed = 20 m/sec
Initial angle is 45°

Solution to May's Problem, 225:

You've got the dirt on us if you answered that Digger will be able to cover his despicable act as long as the hole is 3 ft deep.

Here's how he figured it out:

Digger knew that the volume of the hole less the compacted soil volume needed to equal the volume of the boss.

So, if X= weight of 1 ft3 of maximum density soil,

and 85% maximum density soil is compacted to 90%, its 1 ft3 volume is:

or a reduction of 0.56, So,

Therefore, if the dimensions of the hole are 2 ft X 6 ft,

Digger decided the deed was too dreadful.

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