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A toy rocket is launched straight up from the ground with an initial velocity of 80 ft/s and returns to the ground after 5 seconds. What is the maximum height of the rocket, in feet?

Answer :

The maximum height of the toy rocket launched straight up with an initial velocity of 80 ft/s that returns to the ground after 5 seconds is 100 feet.

To determine the maximum height of a toy rocket that was launched straight up from the ground with an initial velocity and returns to the ground after a certain amount of time, you can use the kinematic equations for uniformly accelerated motion. The relevant equation in this case, assuming acceleration due to gravity (g) is -9.8 m/s2 (converting to feet, approximately -32 ft/s2 since the question provides data in feet) and ignoring air resistance, is:

h = vit + (1/2)at2 where:

  • h is the maximum height
  • vi is the initial velocity (80 ft/s)
  • t is the time it takes to reach the maximum height
  • a is the acceleration due to gravity (-32 ft/s2)

As the rocket is launched upwards and comes to a stop at its peak before coming back down, the time to reach the maximum height is half the total trip time, which is 2.5 seconds. Using the formula, we get:

h = 80 ft/s \\(2.5 s) + (1/2)(-32 ft/s2)(2.5 s)2

h = 200 ft - 100 ft

h = 100 ft

Therefore, the maximum height reached by the rocket is 100 feet.

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Rewritten by : Barada