A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 29.4 . The rocket accelerates for a period of 10.0 before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall.
Find the maximum height, , reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 .
Since the acceleration is constant i used the equation
y=y0+v0t+.5at^2
y0=0
v0t=0
What is acceleration?
would it be 9.81 or 29.4?
The acceleration while thrusting is +29.4 m/s^2. You can use your formula, as written, to compute the height y after 10 seconds. At that time, the acceleration becomes -9.81 m/s^2. The easiest way to compute how much higher it goes after that (delta y)is to take the velocity at t=10 s (Vm = 294 m/s), and assume that the kinetic energy KE gets converted to additional potential energy.
g*delta y = (1/2)Vm^2
ymax = y(10s) + delta y
Acceleration is the rate at which an object's velocity changes. In this case, you have two accelerations involved: the acceleration of the rocket when it is ascending and the acceleration due to gravity when it is in free fall.
When the rocket is ascending, its acceleration is given as 29.4 m/s^2. This is the acceleration generated by the rocket engines.
When the rocket enters free fall, its acceleration is due to gravity, which is 9.81 m/s^2. This is the acceleration experienced by all objects near the Earth's surface.
In the equation you mentioned, which is the equation of motion for constant acceleration, a represents the acceleration. So, when finding the maximum height reached by the rocket, you should use 9.81 m/s^2, as this represents the acceleration due to gravity during free fall.
Let me know if there is anything else I can assist you with.