At a professional sports game, T-shirts are shot out of a small cannon into the crowd. Suppose a T-shirt is shot from 1 meter off the ground with an initial upward velocity of 20 meters per second. The height of the path of the shirt, in meters, is approximated by the function h(t) = −4.9t2 + 20t + 1. Round your answers to the nearest tenth.
10=-4.9t2+20t+1
0=-4.9t2+20t-9
x= −20±√(20)2−4(-4.9)(9)/2(-4.9)
(a) you have asked no question, but it appears you want to know when the height is 10 meters.
(b) leaving your answer in the form shown, with no regard for operator precedence, is poor form.
You did not actually ask a question.
From you opening equation I conclude that you were asking,
" How long would it take to reach a height of 10 m ? "
make sure you include brackets when you do your calculations
4.9t^2 - 20t + 9 = 0 , noticed I multiplied by -1
t = (20 ± √(20^2 - 4(4.9)(9) )/(9.8
= (20 ± 14.953...)/9.8
= appr .5 sec or appr 3.6 seconds
note: the first answer is the time it takes to reach 10 m on its way up, the 3.6 seconds is how long it takes to reach 10 m on its way down
To solve the quadratic equation -4.9t^2 + 20t - 9 = 0, you can use the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = -4.9, b = 20, and c = -9.
Substituting these values into the quadratic formula, we get:
t = (-20 ± √(20^2 - 4(-4.9)(-9))) / (2(-4.9))
Now let's simplify the equation:
t = (-20 ± √(400 - 4(-4.9)(-9))) / (-9.8)
Next, we'll simplify the expression inside the square root:
t = (-20 ± √(400 - 4(4.9)(9))) / (-9.8)
t = (-20 ± √(400 - 176.4)) / (-9.8)
t = (-20 ± √(223.6)) / (-9.8)
Now, we can calculate the square root:
t = (-20 ± 14.94) / (-9.8)
Using rounding to the nearest tenth, we get two possible solutions:
t1 = (-20 + 14.94) / (-9.8) ≈ -0.54
t2 = (-20 - 14.94) / (-9.8) ≈ 3.06
Therefore, the two possible values for t are approximately -0.54 and 3.06.