A rocket blasts off vertically from rest on the launch pad with an upward acceleration of 2.80 . At 30.0 after blastoff, the engines suddenly fail, which means that the force they produce instantly stops.
That is correct. So, what?
To solve this problem, we need to determine the height reached by the rocket before the engines fail. We can use the kinematic equation to solve for the height. The equation we need to use is:
h = u*t + (1/2)*a*t^2
Where:
h = height (unknown)
u = initial velocity (0, as the rocket starts from rest)
t = time (30.0 s)
a = acceleration (2.80 m/s^2)
Plugging in the known values into the equation, we have:
h = 0*(30.0) + (1/2)*(2.80)*(30.0)^2
Simplifying the equation, we get:
h = 0 + (1/2)*(2.80)*(900.0)
h = 0 + 1260.0
Therefore, the height reached by the rocket before the engines fail is 1260.0 meters.