Question

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

Answer 1

The correct answer is D. 5 seconds

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

Answer 2

To answer this item, we just have to substitute the given to the equation, where s is equal to 4 and v is equal to 80 ft/s.
4 = (80)t - 0.5(32 ft/s²)(t²)

The value of t from the equation generated above is equal to 4.94 s. Thus, the answer is approximately 5, letter D.