A test rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and acquired a velocity of How long did the burn phase last?
velocity of ?
To find out how long the burn phase of the rocket lasted, we need to use the kinematic equations of motion. Let's denote the initial velocity as u, final velocity as v, acceleration as a, and time as t.
We know that the rocket is launched vertically, so the acceleration will be in the upward direction, opposite to the gravitational acceleration (-9.8 m/s²). Given that the rocket has risen to a height of 49 m, we can assume that the final velocity is 0 m/s (since it stops at the highest point before falling back down).
We can use the first equation of motion:
v = u + at
Rearranging the equation, we have:
t = (v - u) / a
Given that the initial velocity u is not provided in the question, we cannot directly calculate the time. However, if we assume that the rocket starts from rest (u = 0 m/s), we can calculate the time for this case.
Using the equation, we have:
t = (0 - 0) / (-9.8)
Simplifying, we find:
t = 0 seconds
So, if the rocket started from rest, the burn phase would last 0 seconds. However, if the rocket had some initial velocity, we would need that information to calculate the actual duration of the burn phase.