A model rocket is launched straight upward

with an initial speed of 51.6 m/s. It accelerates with a constant upward acceleration of
1.96 m/s2 until its engines stop at an altitude
of 230 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
Answer in units of m

When does the rocket reach maximumheight?
Answer in units of s

How long is the rocket in the air?
Answer in units of s

To find the maximum height reached by the rocket, we can first determine the time it takes for the rocket to reach maximum height. The equation we can use is:

v = u + at,

where:
v is the final velocity (0 m/s at maximum height),
u is the initial velocity (51.6 m/s),
a is the acceleration (-1.96 m/s^2 since it is directed opposite to the velocity),
and t is the time taken.

From this equation, we can solve for t:

0 = 51.6 + (-1.96)t.

Rearranging the equation, we get:

1.96t = 51.6.

Dividing both sides by 1.96, we find that t ≈ 26.33 seconds.

To find the maximum height reached by the rocket, we can use the following equation:

s = ut + 0.5at^2,

where:
s is the displacement (maximum height reached),
u is the initial velocity (51.6 m/s),
a is the acceleration (-1.96 m/s^2),
and t is the time taken (26.33 s).

Plugging in the values, we have:

s = (51.6)(26.33) + 0.5(-1.96)(26.33)^2.

Evaluating this equation, we find that the maximum height reached by the rocket is approximately 677.35 meters.

Next, to find when the rocket reaches maximum height, we can simply use the value of t we calculated earlier, which is approximately 26.33 seconds.

Finally, to find how long the rocket is in the air, we can double the value of t, since it takes the same amount of time to go up and come back down. Therefore, the rocket is in the air for approximately 52.66 seconds.