A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of 18.4 m/s2. However, after 49.6 seconds of flight the engine fails. Neglect air resistance and assume g = 9.80 m/s2 throughout the flight.
So what are you asking?
To find the maximum height reached by the rocket, we can use the kinematic equation for displacement:
d = v0t + (1/2)a*t^2
Where:
d = displacement (maximum height)
v0 = initial velocity (which is 0 m/s since the rocket is launched from rest)
t = time (49.6 seconds in this case)
a = acceleration (18.4 m/s^2 in this case)
Substituting the given values into the equation, we have:
d = 0 * 49.6 + (1/2) * 18.4 * (49.6)^2
Simplifying the equation gives us:
d = (1/2) * 18.4 * (49.6)^2
Now we can calculate the maximum height reached by the rocket.