Question

When a bottle of champagne is shaken several times, held upright, and uncorked, its cork travels according to the function h(t) = -16t² + 64t + 3. What is the height of the cork at time t?

a) -16t² + 64t + 3
b) 16t² - 64t - 3
c) -16t² - 64t - 3
d) 16t² + 64t + 3

Answer 1

The height of the cork at time t after being uncorked is given by the function h(t) = -16t² + 64t + 3, making option a) the correct answer.

Step-by-step explanation:

The height of the cork at time t, when a bottle of champagne is shaken, held upright, and uncorked, is given by the function h(t) = -16t² + 64t + 3. This function represents the cork's trajectory with time being the variable t.

The correct answer is option a) -16t² + 64t + 3, as it directly matches the function provided for the height h(t) of the cork at any given time t.

For example, if we want to find the height at t = 1 second, we would substitute 1 into the function:

h(1) = -16(1)² + 64(1) + 3

= -16 + 64 + 3

= 51

So, the height of the cork at time t = 1 second is 51 units.