Question

20 POINTS

Ryan throws a baseball upward with an initial velocity of 12 m/s from a height of 2m above the ground. How long will it take for the baseball to hit the ground? Round answer to the nearest 10th of a second.

Answer 1

2.6 seconds

Explanation:

g = 10

s = 2

u = -12

t = ?

2 = -12t + 5t²

5t² - 12t - 2 = 0

t = [12 +/- sqrt(12² - 4(5)(-2)]/2(5)

t = (12 +/- sqrt(184))/10

t = 2.55646599663

Answer 2

Explanation:

Our function, in terms of the gravitational pull in the metric system, will be

`s(t)=-4.9t^2+12t+2`

where the leading coefficient represents the acceleration due to gravity (if you do not know calculus, just take me at my word on this!), 12 is the initial vertical velocity, and 2 is the initial height of the baseball. Being asked the question, "How long will it take for the ball to hit the ground?" is the exact same as being asked, "How long was the ball in the air?" Be aware of the wording!!

s(t) represents the height of the ball at a certain time during its flight. If the ball hits the ground, we know that the height of something ON the ground is 0, so sub in 0 for s(t) and factor to solve for t.

If you throw this into the quadratic formula, you get that

t = -.2 seconds and t = 2.6 seconds.

Since time will NEVER be negative, we know that it takes the ball 2.6 seconds to hit the ground. It was also, then, in the air for 2.6 seconds.