Please Help Algebra Word Problem

Question

An arrow is shop upward from a platform 40ft high with an initial velocity of 224 ft per sec. Its height h in feet after t seconds is given by the equation below. At what time will the arrow be at 824 ft above the ground.

h= -16t^2 + 224t + 40

Answer 1

824 = -16t² + 224t + 40

Set equal to zero and solve for t.

Answer 2

An arrow is shop upward from a platform 40ft high with an initial velocity of 224 ft per sec. Its height h in feet after t seconds is given by the equation below. At what time will the arrow be at 824 ft above the ground.

h= -16t^2 + 224t + 40

h is given in the problem as 824 ft.....so....when h = 824 you want to know the value of t.....so.....

substitute the value 824 in the formula and SOLVE for t....we have....

824 = -16 t² + 224t + 40.......subtract 824 from both sides we have......

-824 -824

0 = -16t2 + 224t - 784

-------------USE QUADRATIC FORMULA to compute the t values---------

t =( - b +/- √b² - 4 a c )/2a

t = (-224 +/- √224² - 4 (-16)(-784)) / 2 (-16)

t = -224 +/- √50176 - 50176 / -32

t = -224 +/- √0 / -32 = -224/-32 = 7

t = 7

where the coefficients taken from the formula above are

a = -16

b = 224

c = -784

So in this you have t = 7 seconds......

Quadratic Formula taken from this website....

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php