Question

A model rocket is launched with an initial upward velocity of 175/fts. The rocket's height h (in feet) after t seconds is given by the following h=175t - 16t^2. Find all values of for which the rocket's height is 85 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Answer 1

Answer:

0.51 second or 10.43 second

Explanation:

$h = 175 t - 16t^{2}$

Put h = 85 feet

$16t^{2} - 175 t + 85 = 0$

Solve the equation and find the values of t

$t = \frac{175\pm \sqrt{(-175)^{2}-4\times 16\times 85)}}{2\times 16}$

t = 0.51 second or 10.43 second

Answer 2

Two values of time will be t1 = 10.42 seconds or t2 = 0.51 seconds

What is a quadratic equation ?

A quadratic equation is an equation containing a single variable of degree 2. Its general form is ax2 + bx + c = 0, where x is the variable and a, b, and c are constants (a  is not equal to 0).

Rocket's height h (in feet) after t seconds is  h=175t - 16t^2

to find

All values of for which the rocket's height is 85 feet =?

putting h= 85 feet

85 = 175t - 16$t^{2}$

16$t^{2}$ - 175 t + 85 =0

since , it is a quadratic equation , need to find its roots

D = $b^{2}$ - 4ac

   = $(-175)^{2}$  - 4 * (16) * 85 = 25185

since , value of D of this quadratic equation is greater than 0 , it will have real and distinct roots

t1 = (-b + $\sqrt{D}$) / 2a

  = (- (-175) + 158.70 ) / 2* 16 = 10.42 seconds

t2 =  (-b - $\sqrt{D}$) / 2a

    = (- (-175) - 158.70 ) / 2* 16 = 0.51 seconds

Two values of time will be t1 = 10.42 seconds or t2 = 0.51 seconds

learn more about quadratic equation

https://brainly.com/question/17177510?referrer=searchResults

#SPJ2