word problem

Question

a ball is thrown vertically upward from the ground. its distance in feet from the ground in t seconds is s=16t^{^2}+192t. After how many seconds will the ball be 432 feet from the ground?

Answer 1

The equation in the problem statement is not correct. It should be

s(t) = -16t² + 192t,

assuming the ball is thrown at an initial upward speed of 192 ft/s.  Then set s(t) = 432, obtain a quadratic equation in t, and solve for t using the quadratic formula.  You will get 2 positive solutions for t.  The lower solution will be the time in seconds that it takes to reach 432 ft on the way up, and the higher solution will be the time it takes to reach 432 ft again, but on the way down.

Answer 2

So the question is asking at what time "t" will the balls distance from the ground be 432 

 

In other words, when does the 16t²+192t=432? So solve the quadratic equation by the quadratic formula, factoring, or completing the square. Once you do that you get that t=1.9372539331938 seconds. Does the question ask you to round?