A bottle rocket is launched upward at 128 feet per second from a platform that is 136 feet high. Its path can be mapped by the equation h = - 16t^2 + v'o't + h'o (where h=height, t=time, v'o=initial velocity, and h'o=initial height).

Which of the following equations represents the height of the rocket in vertex form?

A. h=-16 (t-8) ^2+136

B. h=-16 (t^2-8t) + 136

C. h=16 (t-4) ^2

D. h=-16 (t-4) ^2+392

Question

Mathematics

Raquel Garcia

11 November, 17:25

A bottle rocket is launched upward at 128 feet per second from a platform that is 136 feet high. Its path can be mapped by the equation h = - 16t^2 + v'o't + h'o (where h=height, t=time, v'o=initial velocity, and h'o=initial height).

Which of the following equations represents the height of the rocket in vertex form?

A. h=-16 (t-8) ^2+136

B. h=-16 (t^2-8t) + 136

C. h=16 (t-4) ^2

D. h=-16 (t-4) ^2+392

+1

Answers (1)

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Jones · Answer 1

D2x/dt2=-g (which we'll approximate as a constant - 32ft/s^2)

d2x/dt2=-32 integrating we get:

dx/dt=-32t+C, where C is the initial velocity which we are told is 128ft/s so

dx/dt=-32t+128, integrating again we get:

h (t) = - 16t^2+128t+C, where C is the initial height of the object ... which we are told is 136 ft so

h (t) = - 16t^2+128t+136 if we factor the first two terms we get:

h=-16 (t^2-8t) + 136