A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base wi
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- čas přidán 29. 08. 2024
- A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.
(a) At what rate is his distance from second base decreasing when he is halfway to first base?
(b) At what rate is his distance from third base increasing at the same moment?
![How to Solve ANY Related Rates Problem [Calc 1]](http://i.ytimg.com/vi/gBHIZlF0TX8/mqdefault.jpg)
why is third spelled out but first and second aint
For part A, since it is asking for the rate at which the distance is decreasing, wouldn't it just be positive 24/sqrt5? It would only be negative if it was asking for the rate of change, but the word decreasing cancels out the negative sign.
+Peter Yang Excellent point, yes!
I don't understand why you couldn't just labeled half the distance of the 90 ft side 45 ft rather than x or 90-x. Isn't it obvious?
Because you only plug in the 45 after having differentiated the pythagorean equation. If you were to initially plug in the 45, to make it 45^2 + 90^2 = a^2, then that equation assumes the initial length from home to 1st base is 45ft in total instead of 90, thus making it not a square anymore. If you were to differentiate that, you’d get 0.
Remember, setting up the equation is just setting up the relation between quantities, you only plug in your given values after having differentiated the equation, not before.
Congratulations on the excellent resolution of this problem. I was unable to solve these problems like that. Could help me?
In a baseball game (which is played on a square-shaped Diamond 90 feet on each side) between the Brewers and the Cubs, Joe (who is playing left field for the Brewers) hits the ball while at bat and runs toward first base at the rate of 20 feet per second. Just as Joe starts toward first base, his teammate Tony, who had taken a 10-foot lead off second base, starts running toward third base at the same rate of speed. How fast is the distance between Joe and Tony changing at the instant when Tony reaches third base? (MUNEM & FOULIS, problem 16; p.225)
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The baseball diamond is NOT square. It's not 90 degrees. 2nd base is slightly further out, therefore it's a baseball DIAMOND, not a baseball SQUARE.
It literally says in the problem that the diamond IS a square.
@@FytchVz I know that. That's why I posted the comment. It's not square. The angles at 1st and 3rd base are not 90 degrees. If you care to learn, you can Google it.
Isn't a batter batting at home base?? haha Great video though!
thanks againn!!!!
You're welcome again!
Thanks dude!!!
How come in the ship question when b had a value, you took the derivative of b^2 and plugged in the value of b, but here you took the derivative of the value of b which was 90 to 0, instead of b^2
because the derivative of 90 was 0, I first substitute it in before derivative.
I really need some help
in my hw i had a rate of 28ft/s and it wanted it to the tenth and I got -12.5 and i have no idea why its wrong
it's right, but it should be positive (like peter said in the comments: since the distance is decreasing, it's positive 24/sqrt 5). the negative is already implied. so the rate decreasing is 12.5. Be aware that if it says rate of change, you should write -12.5
to add the 90-x should actually be in the first problem. Check out: cda.mrs.umn.edu/~mcquarrb/teachingarchive/M1101/HW/3.9.pdf
Wrong, the first triangle you made at 1 minute 16 seconds is 90-x not just x. so It should be( 90-x) squared+90 squared = a squared!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Nope, he's correct. The side of the triangle is (90-x) + x = 90, and he's solving by using x first. Either way, it's the same result if you want to do it your way and use x for triangle 2.