The function s(t) = vt + h - 0.5at^2 represents the height of an object, s, from the ground after the time, t, when the object is thrown with an initial velocity of v at an initial height of h and where a is the acceleration due to gravity (32 feet per second squared).

a baseball player hits a baseball 4 feet above the ground with an initial velocity of 80 feet per second. about how long will it take the baseball to hit the ground?

a. 2 seconds
b. 3 seconds
c. 4 seconds
d. 5 seconds

The correct answer is D. 5 seconds

Step-by-step explanation:

The function is given to be : s(t) = vt + h - 0.5at²

where, s represents the height of the object from the ground after time t, v represents the initial velocity , a is the acceleration due to gravity which is to be taken 32 feet/sec²

Now, s = 4 feet

Initial velocity, v = 80 feet/second

a = 32 feet/sec²

⇒ s(t) = vt + h - 0.5at²

⇒ 4 = 80 × t - 0.5 × 32 × t²

⇒ 16t² - 80·t + 4 = 0

⇒ 4t² - 20t + 1 = 0

⇒ t = 4.95 seconds

⇒ t ≈ 5 seconds

Hence, It will take approximately 5 seconds for the baseball to hit the ground

Therefore, The correct answer is D. 5 seconds

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it