Answer:
60 seconds
Step-by-step explanation:
step 1.) find how many meters it falls per second
40m / 4sec = 10m/s
step 2.) use the equation above to find in terms of the question
10m/s for 6sec = 10 x 6 ====> 60 seconds
Answer:
the answer is <em><u>1</u></em><em><u>1</u></em><em><u>7</u></em><em><u>8</u></em><em><u>8</u></em> :) your welcome
1 plus 2 = 3, then u do 6/2 (3), then 3x3 = 9
Answer:
Step-by-step explanation:
5+1+3+8+2=19
3/19 = 16%
Here's our equation.
![h=-16t+64t+3](https://tex.z-dn.net/?f=h%3D-16t%2B64t%2B3)
We want to find out when it returns to ground level (h = 0)
To find this out, we can plug in 0 and solve for t.
![0 = -16t+64t+3 \\ 16t-64t-3=0 \\ use\ the\ quadratic\ formula\ \frac{-b\±\sqrt{b^2-4ac}}{2a} \\ \frac{-(-64)\±\sqrt{(-64)^2-4(16)(-3)}}{2*16} = \frac{64\±\sqrt{4096+192}}{32}](https://tex.z-dn.net/?f=0%20%3D%20-16t%2B64t%2B3%20%5C%5C%2016t-64t-3%3D0%20%5C%5C%20use%5C%20the%5C%20quadratic%5C%20formula%5C%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%20%5C%5C%20%5Cfrac%7B-%28-64%29%5C%C2%B1%5Csqrt%7B%28-64%29%5E2-4%2816%29%28-3%29%7D%7D%7B2%2A16%7D%20%20%3D%20%5Cfrac%7B64%5C%C2%B1%5Csqrt%7B4096%2B192%7D%7D%7B32%7D)
![= \frac{64\±\sqrt{4288}}{32} = \frac{64\±8\sqrt{67}}{32} = \frac{8\±\sqrt{67}}{4} = \boxed{\frac{8+\sqrt{67}}{4}\ or\ 2-\frac{\sqrt{67}}{4}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B64%5C%C2%B1%5Csqrt%7B4288%7D%7D%7B32%7D%20%3D%20%5Cfrac%7B64%5C%C2%B18%5Csqrt%7B67%7D%7D%7B32%7D%20%3D%20%5Cfrac%7B8%5C%C2%B1%5Csqrt%7B67%7D%7D%7B4%7D%20%3D%20%5Cboxed%7B%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%5C%20or%5C%202-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%7D)
So the ball will return to the ground at the positive value of
![\boxed{\frac{8+\sqrt{67}}{4}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%7D)
seconds.
What about the vertex? Simple! Since all parabolas are symmetrical, we can just take the average between our two answers from above to find t at the vertex and then plug it in to find h!
![\frac{1}2(\frac{8+\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(2+\frac{\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(4) = 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D2%28%5Cfrac%7B8%2B%5Csqrt%7B67%7D%7D%7B4%7D%2B2-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D2%282%2B%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%2B2-%5Cfrac%7B%5Csqrt%7B67%7D%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D2%284%29%20%3D%202)