A model rocket is fired vertically from the ground with a constant acceleration of 44.3 m/s2 for 1.95 s at which time its fuel is exhausted. What is the maximum height (in m) reached by the rocket?

Shouldn't this just be d=rt?
44.3(1.95), but I'm not getting the right distance, am I supposed to account for gravity?

let's assume that for the first 1.95 seconds, the given acceleration of 44.3 m/s^2 includes the effect of gravity, and for any time thereafter the effects of gravity of -4.9 m/s^2 takes over

for the first part:
a = 44.3
v = 44.3t + c
but when t = 0 (at the start)
v = 0 , ----> c = 0

v = 44.3t
s = 22.15t^2 + k
again, when t = 0 , s - 0 , so k = 0

distance covered = s = 22.15t^2 , where 0≤t≤1.95
so after 1.95 s
the height is 22.15(1.95)^2 = 84.225
and v = 44.3(1.95) = 86.385 m/s

second part:

so the effective height equation after 1.95 s:
height = -4.9t^2 + 86.385t + 84.228 , where t is the time AFTER 1.95 seconds
this is a downwards opening parabola, all we have to do is find its vertex
the t of the vertex is -b/(2a) = -86.385/-9.8 = 8.815 seconds
and the height = -4.9(8.815)^2 + 86.385(8.815) + 84.228
= 464.96 or appr 495 m

remember that the time of 8.815 is the time after the initial 1.95 seconds
so the rocket reaches the maximum of 495 m in 10.765 seconds after take-off.

better check my arithmetic.

To find the maximum height reached by the rocket, you need to consider both the rocket's upward acceleration and the effects of gravity. Since the rocket is fired vertically upwards, it will experience a constant acceleration due to its engine. However, once its fuel is exhausted, it will only be subject to the force of gravity pulling it downwards.

Here's how you can find the maximum height:

1. First, calculate the velocity the rocket reaches when its fuel is exhausted. Since the rocket has a constant acceleration of 44.3 m/s^2 for 1.95 seconds, you can use the following formula to find the final velocity (v) at that time:
v = u + at
where u is the initial velocity (assumed to be 0 because the rocket starts from rest) and a is the acceleration.
v = 0 + 44.3 * 1.95

2. Once you have the final velocity, you can find the time it takes for the rocket to reach maximum height (upward motion) by using the following formula:
v = u + at
where u is the initial velocity (which is the final velocity when the fuel is exhausted because the rocket continues upwards) and a is the acceleration due to gravity (approximately 9.8 m/s^2).
0 = v + (-9.8 * t)
Solve for t to find the time it takes for the rocket to reach maximum height.

3. Now that you know the time it takes for the rocket to reach maximum height, you can find the maximum height (h) using the formula:
h = ut + (1/2)at^2
where u is the initial velocity (v when the fuel is exhausted) and a is the acceleration due to gravity (approximately -9.8 m/s^2).
Plug in the values and calculate the maximum height.

Remember to consider the negative sign when dealing with the acceleration due to gravity, as it is acting in the opposite direction to the rocket's initial velocity.

Using these steps, you should be able to determine the maximum height reached by the rocket.