Final answer:
The final velocity of the model rocket is approximately 59.68 m/s, calculated using the given initial velocity, time, and derived acceleration from the distance covered.
Step-by-step explanation:
The student is asking about the final velocity of a model rocket that is already moving with an initial velocity. To solve this, we need to use the kinematic equation that relates initial velocity, acceleration, and time to the final velocity:
v = vo + at
Where v is the final velocity, vo is the initial velocity (in this case 7 m/s), a is the acceleration, and t is the time. However, the acceleration is not provided directly, but we can calculate it using the information that the rocket climbs 200 m in 6 seconds. Using one of the other kinematic equations:
s = vote + ½at²
We have s (distance climbed) = 200 m, vo (initial velocity) = 7 m/s, and t (time) = 6 seconds. Plugging these into the distance equation and solving for a, we get:
200 m = (7 m/s)(6 s) + ½a(6 s) ²
a = (200 m - (7 m/s)(6 s)) / (0.5*(6 s) ²)
a = (200 m - 42 m) / 18 s²
a = 8.78 m/s² approximately
Now that we have the acceleration, we can find the final velocity using the first equation:
v = (7 m/s) + (8.78 m/s²)(6 s)
v = 7 m/s + 52.68 m/s
v = 59.68 m/s approximately
So, the final velocity of the model rocket is 59.68 m/s approximately.