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Answer :
The rocket will take approximately 3.23 seconds to reach its maximum height or fall back to the ground.
If the initial vertical velocity of a model rocket launched from the ground is 104 feet per second, how long will it take for the rocket to reach its maximum height or fall back to the ground?
To determine the time it will take for the rocket to reach its maximum height or fall back to the ground, we need to consider the motion of the rocket under the influence of gravity.
Initial vertical velocity of the rocket (v₀) = 104 feet per second
In the absence of air resistance, the rocket's motion can be described using the kinematic equation:
h = v₀t + (1/2)gt²
h is the height (displacement),
v₀ is the initial velocity,
t is the time, and
g is the acceleration due to gravity (approximately 32.2 feet per second²).
At the maximum height, the rocket will momentarily come to rest before falling back to the ground. This means its final vertical velocity (v) will be zero.
Using this information, we can set v = 0 and solve for t:
0 = v₀ - gt
gt = v₀
t = v₀ / g
Substituting the given values:
t = 104 feet per second / 32.2 feet per second²
t ≈ 3.23 seconds
Therefore, it will take approximately 3.23 seconds for the rocket to reach its maximum height or fall back to the ground.
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