Please help me solve this word problem (NEED HELP ASAP!!!!)

Question

The height of an object shot straight up with an initial velocity of v in feet per second is given by h + -16ft² +vt + c, where c is the initial height of the object above the ground. The ringer on a carnival strength test is 2 feet above the ground and is shot upward of 30 feet per second. Will it reach a height of 20 feet? Use the discriminant to explain your answer.

Answer 1

First, let us edit the given height equation:

 

h(t) = -16t^2 + vt +c

 

For c = 2 ft and v = 30 ft/s,

 

h(t) = -16t^2 + 30t + 2

 

Let h = 20 ft, and solve for t.

 

20 = -16t^2 + 30t + 2

 

-16t^2 + 30t - 18 = 0

 

8t^2 - 15t + 9 = 0

 

D = discriminant = (-15)^2 - 4(8)(9) = -63

 

D = -63 < 0, so there is no real solution, and the object will not reach 20 ft