the distance traveled by the ball is given by

D(t)=-5t^2+115t-110 (in feet)

how far will the ball travel before it hits the ground?

at what level is ground?

this informations I have:

The Physics of Baseball by Robert Adair -
after t seconds, starting 1 sec after 35 angle, rotating with an initial backspin of 2000 revolutions per minute, and hit about 110mph is given by
H(t)= -80t^2+340t-260 (in feet)

a)how many seconds willpass before the ball hits the ground?

The distance travelded by the ball is given by
D(t)= -5t^2+115t-110 (in feet)

b)How far will the ball travel before it hits the ground?

c)Using D(t), how far will a ball travel in 6 seconds, the time it takes it takes a high fly ball to hin the ground?

To find how far the ball will travel before hitting the ground, we need to determine the time at which the ball hits the ground. In this case, the ball hits the ground when its height, represented by the function D(t), becomes zero.

D(t) = -5t^2 + 115t - 110

To find when D(t) = 0, we need to solve the equation:

-5t^2 + 115t - 110 = 0

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the values of t:

t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -5, b = 115, and c = -110. Plugging in these values, we get:

t = (-115 ± √(115^2 - 4(-5)(-110))) / (2(-5))

Simplifying further:

t = (-115 ± √(13225 - 2200)) / (-10)
t = (-115 ± √(11025)) / (-10)
t = (-115 ± 105) / (-10)

Now, let's calculate the two possible values of t:

t1 = (-115 + 105) / (-10) = -10/(-10) = 1
t2 = (-115 - 105) / (-10) = -220/(-10) = 22

Therefore, the ball hits the ground at either t = 1 second or t = 22 seconds. To find how far the ball travels before hitting the ground, we need to substitute these values back into the D(t) equation:

D(1) = -5(1)^2 + 115(1) - 110
D(1) = -5 + 115 - 110
D(1) = 0

D(22) = -5(22)^2 + 115(22) - 110
D(22) = -5(484) + 115(22) - 110
D(22) = -2420 + 2530 - 110
D(22) = 0

Both calculations yield zero, indicating that the ball hits the ground at both t = 1 second and t = 22 seconds. Therefore, the ball travels a distance of 0 feet before hitting the ground.