In major league baseball, a fastball travels the distance (60 ft 6 in) from the pitcher to the catcher in 0.41 s. On average, a batter connects with the ball 0.28 s after the start of the swing. Using these figures, estimate how long the ball is in range to be hit by the batter. In other words, by how much time can the batter be off in the start of the swing and still hit the ball?
2007-09-10 05:33:55 · 3 answers · asked by billie jean 1 in Science & Mathematics ➔ Mathematics
No, there is enough information. You can use the distance formula (d=rt). I've partially done this problem out, but I keep disregarding the .28 s. I just don't know what to do, and my teacher won't help me. All he told us was that it's going to be on the chapter test, so we better be able to do it right.
2007-09-10 05:51:17 · update #1
The length (from the very tip) of home plate is 17 inches.
And the distance from the pitcher to the catcher is 726 inches.
2007-09-10 06:44:11 · update #2
The answer should be an inequality.
Probably something like 5 is less than or equal to x which is less than or equal to 10. (This is just an example, obviously.)
2007-09-10 07:54:53 · update #3
First I'm going to make some assumptions. The ball can be hit successfully if it is within one foot of the centreline of the plate.
Second the bat travells in an arc and strikes the ball near the tip. The bat tip travels through an arc of approx 6' radius and strikes the ball after approximately 180 degrees of rotation throughout the arc (or about 9.4' of travel).
Third the bat accelerates at a constant rate until it strikes the ball. The acceleration is given by
x = 1/2 a t^2
9.4 = 1/2 a (0.28)^2
a = 240 feet per sec per sec
Speed of the bat tip is 67 feet per sec
Now the ball is travelling at (60.5 feet / .41 sec) or 148 feet per second.
Since I estimated the hitting zone to be 1' either side of the centre of the plate. The latest the ball could still be hit is the time taken for the ball to travel the extra foot plus the time saved by the bat travelling one foot less. or 1/148 + 1/67 = 0.015 of a second.
Answer is the batter can be up to 15 milliseconds off and still hit the ball.
This assumes that the batter cannot adjust the speed of his swing following visual queues which I think is not 100% correct.
2007-09-10 06:16:27 · answer #1 · answered by Ben O 6 · 0⤊ 0⤋
Assuming the ball is in the strike zone, and that the strike zone is about 3 feet long, the ball will be in the strike zone for only .02 seconds. Hence he has a leeway of .02 seconds
2007-09-10 12:54:46 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
Not enough information.
2007-09-10 12:41:58 · answer #3 · answered by gebobs 6 · 0⤊ 0⤋