Final answer:
It will take approximately 6.37 seconds for the rocket to reach a velocity of 0.00 m/s after being launched with a velocity of 62.5 m/s and decelerating due to gravity at -9.81 m/s².
Step-by-step explanation:
A model rocket launches with a vertical velocity of 62.5 m/s and is subjected to an acceleration due to gravity of -9.81 m/s². To determine how long it will take for the rocket to have a velocity of 0.00 m/s, we can use the kinematic equation:
v = v0 + at
Where:
- v is the final velocity (which is 0 m/s in this case)
- v0 is the initial velocity (62.5 m/s)
- a is the acceleration (-9.81 m/s²)
- t is the time which we want to find
Rearrange the formula to solve for time (t):
t = (v - v0) / a
Substitute the known values:
t = (0 m/s - 62.5 m/s) / (-9.81 m/s²) = 6.37 seconds
Therefore, it will take approximately 6.37 seconds for the rocket to reach a velocity of 0.00 m/s.