SOLUTION: Stephanie is the star of her softball team. Last week she hurt her knee a bit as she slid into home, so she had taped her knee for yesterday's game. Her knee as a little stiff, so

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Question 1147934: Stephanie is the star of her softball team. Last week she hurt her knee a bit as she slid into home, so she had taped her knee for yesterday's game. Her knee as a little stiff, so she could only run 5 miles per hour yesterday, which is slower than her usual running speed. Midway through the game, she was at second base, with a 5-foot leed off the base. The distance from second base to third base measured 60 feet. The pitcher pitched the ball, which traveled at 60 miles per hour. The distance from the pitchers mound to home plate was 45 feet. Stephanie started running to third base the moment the pitcher pitched the ball. When the ball reached home plate, the batter hit the ball and it traveled at 75 miles per hour, directly to the right fielder who was 180 feet away from home plate. The right fielder dropped the ball, then picked it up and threw it to third base. It took 2.5 seconds for the right fielder to drop the ball, pick it up, and release the throw. She threw the ball at 45 miles per hour to third base, which was 170 feet away. The third baseman caught the ball and tagged stephanie. The act of catching the ball and applying the tag took 0.5 seconds. Was stephanie safe or out?
Answer by VFBundy(438) About Me  (Show Source):
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With a 5-foot lead off of second base, and with the distance between second and third base being 60 feet, this means Stephanie is 55 feet from third base.

So, as far as Stephanie goes, we have the distance (55 feet) and the rate of speed (5 mph). So, we are looking for the time. How long does it take her to get to third base?

We need to figure out how many "feet per second" that "5 miles per hour" is. We do it as such:

5+miles%2Fhour = 5%285280+feet%29%2F3600+seconds = 26400+feet%2F3600+seconds = 22+feet%2F3+seconds = 22/3 feet per second

So, Stephanie's speed is 22/3 feet per second. Now, we have:

Distance = 55 feet
Rate = 22/3 feet per second
Time = t seconds

Time = Distance%2FRate

Time = 55%2F%2822%2F3%29 = 3%2855%29%2F22 = 165/22 = 15/2 = 7.5

So, now we know that it takes Stephanie 7.5 seconds to run to third base.

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We know that Stephanie starts running to third base the moment the pitcher pitches the ball. For all of the following, we are looking for the time. How long do each of these steps take?

The pitcher pitched the ball, which traveled at 60 miles per hour. The distance from the pitchers mound to home plate was 45 feet.

Again, to get the rate, we need to convert "miles per hour" into "feet per second":

60+miles%2Fhour = 60%285280+feet%29%2F3600+seconds = 316800+feet%2F3600+seconds = 88+feet%2Fsecond = 88 feet per second

So, we have:

Distance = 45 feet
Rate = 88 feet per second
Time = t seconds

Time = Distance%2FRate

Time = 45/88 = 0.5114 seconds

So, it takes 0.5114 seconds for the ball to be pitched to home plate.

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When the ball reached home plate, the batter hit the ball and it traveled at 75 miles per hour, directly to the right fielder who was 180 feet away from home plate.

Converting "miles per hour" into "feet per second":

75+miles%2Fhour = 75%285280+feet%29%2F3600+seconds = 396000+feet%2F3600+seconds = 110+feet%2Fsecond = 110 feet per second

So, we have:

Distance = 180 feet
Rate = 110 feet per second
Time = t seconds

Time = Distance%2FRate

Time = 180/110 = 18/11 = 1.636 seconds

So, it takes 1.636 seconds for the ball to be hit to the right fielder.

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The right fielder dropped the ball, then picked it up and threw it to third base. It took 2.5 seconds for the right fielder to drop the ball, pick it up, and release the throw.

Obviously, this part takes 2.5 seconds.

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The right fielder threw the ball at 45 miles per hour to third base, which was 170 feet away.

Converting "miles per hour" into "feet per second":

45+miles%2Fhour = 45%285280+feet%29%2F3600+seconds = 237600+feet%2F3600+seconds = 66+feet%2Fsecond = 66 feet per second

So, we have:

Distance = 170 feet
Rate = 66 feet per second
Time = t seconds

Time = Distance%2FRate

Time = 170/66 = 85/33 = 2.576 seconds

So, it takes 2.576 seconds for the right fielder's throw to reach third base.

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The third baseman caught the ball and tagged Stephanie. The act of catching the ball and applying the tag took 0.5 seconds.

Obviously, this part takes 0.5 seconds.

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So, now we need to add all these parts together to see how long they take as a whole:

Ball being pitched to home plate = 0.5114 seconds
Ball being hit to right fielder = 1.636 seconds
Ball being dropped by right fielder = 2.5 seconds
Ball being thrown by right fielder to third base = 2.576 seconds
Third baseman catching ball and applying tag = 0.5 seconds

0.5114 + 1.636 + 2.5 + 2.576 + 0.5 = 7.7234 seconds

Since it took Stephanie only 7.5 seconds to run to third base, this means she was SAFE.