The function g(t) = -16t2 + vt + h represents the height of an object, g, in feet above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet.
A model rocket is launched off the ground at an initial velocity of 60 feet per second.
Write a function that can be used to describe the flight of the model rocket.
A.g(t) = -16t2 + 60t
B.g(t) = -16t2 + t + 60
C.g(t) = -16t2 + 60t + 60
D.g(t) = -16t2 + 60
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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
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