Question

A model rocket is launched from the ground with an initial velocity of 100 feet per second. How many seconds later does the rocket hit the ground?

Enter your answer as a number rounded to the nearest tenth, such as: 42.5

Answer 1

Answer:

  6.3

Step-by-step explanation:

The rocket hits the ground at the same speed it left, only the velocity is downward, rather than upward. That is, the change in velocity is from +100 ft/s to -100 ft/s, a total change of 200 ft/s. The change in velocity is brought about by the acceleration due to gravity, 32 ft/s/s. The time required for the observed change in velocity is ...

  (200 ft/s)/(32 ft/s²) = 6.25 s

Rounded to tenths, it takes the rocket 6.3 seconds to hit the ground.

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The equation for the ballistic motion of the rocket is ...

  h(t) = -1/2·gt² +v0·t

where g is 32 ft/s² and v0 is 100 ft/s. A graph of this equation shows the rocket hits the ground at 6.25 seconds, as above.