A space aircraft is launched staight up.The aircraft motor provide aconstant acceleration for 10 second ,then it stops.the aircraft's altitude 15 second after launch is 2 km.ignore air friction.what is the acceleration and the maximum speed reached in km/h?
To determine the acceleration and maximum speed reached by the space aircraft, we can use the equations of motion.
Let's break down the given information:
Initial velocity (u) = 0 (since the aircraft is launched straight up)
Acceleration (a) = unknown
Time (t) = 10 seconds (the duration for which the acceleration is provided)
Final velocity (v) = unknown
Altitude (s) = 2 km = 2000 meters
1. Calculate the acceleration:
We can use the equation of motion: s = ut + (1/2)at^2
Substituting the given values, we have: 2000 = 0 + (1/2)(a)(10^2)
Simplifying, we get: 2000 = 50a
Dividing both sides by 50, we find: a = 40 m/s^2
Therefore, the acceleration of the space aircraft is 40 m/s^2.
2. Calculate the maximum speed:
The maximum speed occurs when the acceleration stops, so we need to determine the final velocity at that point. Given that the acceleration stops after 10 seconds:
Using the equation of motion: v = u + at
Substituting the values, we have: v = 0 + (40)(10) = 400 m/s
To convert the final velocity to km/h, multiply by 3.6 (since 1 m/s = 3.6 km/h):
400 m/s * 3.6 = 1440 km/h
Therefore, the maximum speed reached by the space aircraft is 1440 km/h.
In conclusion, the acceleration of the aircraft is 40 m/s^2, and the maximum speed reached is 1440 km/h.