Question

NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t2 +255. What would be the effect of h(t) - k, if k = 45?​ A) The rocket's height, relative to sea level, will be 45 meters lower at all times.

B) The rocket's height will be 45 meters higher at all times.
C) The rocket's height will remain the same; there will be no effect.
D) The rocket's height will vary with time in a complex manner due to the subtraction, making it unpredictable.

Answer 1

Subtracting a constant k = 45 from the height function h(t) = -4.9t^2 + 255 lowers the rocket's height by 45 meters at all times.

Step-by-step explanation:

If the height function h(t) of a rocket is given by h(t) = -4.9t2 + 255 and we subtract a constant k from the function, the new height function would be h(t) - k. Given that k = 45, the new function will be h(t) - 45 = -4.9t2 + 210. Subtracting 45 from the height function essentially lowers the entire graph of the function by 45 meters. This means at every point in time t, the height of the rocket will be 45 meters lower than it would be without subtracting 45. Therefore, option A is correct: The rocket's height, relative to sea level, will be 45 meters lower at all times.