A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms
Balls height ![h= 2 +9t -5t^2](https://tex.z-dn.net/?f=%20h%3D%202%20%2B9t%20-5t%5E2%20)
To find all values of t for which the ball's height is 3 meters
We plug in 3 for h and solve for t
![h= 2 +9t -5t^2](https://tex.z-dn.net/?f=%20h%3D%202%20%2B9t%20-5t%5E2%20)
![3 = 2 +9t -5t^2](https://tex.z-dn.net/?f=%203%20%3D%202%20%2B9t%20-5t%5E2%20)
Solve for t
![0= -1+ 9t -5t^2](https://tex.z-dn.net/?f=%200%3D%20-1%2B%209t%20-5t%5E2%20)
![5t^2 - 9t + 1 = 0](https://tex.z-dn.net/?f=%20%20%20%205t%5E2%20-%209t%20%2B%201%20%3D%200%20)
Solve using quadratic formula
![t= \frac{-b+- \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=%20t%3D%20%5Cfrac%7B-b%2B-%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%20%20)
![t= \frac{9+- \sqrt{(-9)^2-4*5*1} }{2*5}](https://tex.z-dn.net/?f=%20t%3D%20%5Cfrac%7B9%2B-%20%5Csqrt%7B%28-9%29%5E2-4%2A5%2A1%7D%20%7D%7B2%2A5%7D%20%20)
After simplifying this,
= 0.11898
= 1.68102
the values of t for which the ball's height is 3 meters= 0.12 sec , 1.68 sec
Answer:
-2b and -0.9b and b/12
Step-by-step explanation:
I'd suggest you write "6 2/5," not "6 and 2/5."
6 2/5 rotations
-------------------- =
2 2/3 seconds
32
---
5 32 3
------- = ------ * -----
8 5 8 Reduce that 32/8: obtain 4.
---
3
Then we have
4(3)/5, or 12/5 rotations per sec.