A model rocket is launched straight upward with an initial speed of 52 m/s. It acceler- ates with a constant upward acceleration of 2.6 m/s2 until its engines stop at an altitude of 202.2 m.
What is the maximum height reached by the rocket?
Answer in units of m
How long after lift-off does the rocket reach its maximum height? Answer in units of s
How long is the rocket in the air? Answer in units of s
power phase
v = 52 + a t
h = 52 t + (1/2) 2.6 t^2 = 52 t + 1.3 t^2= 202.2
solve for t with quadratic eqn
v = 2.6*t = use t to get it. This is vi for next pahse
ballistic phase
hi = 202.2
vi = from power phase
a = -9.8
v = 0 at top = vi -9.8 t
solve for t in this phase
then
h = 202.2 + vi t - 4.9 t^2
after calculating all that i came to a max height of 206.59m but supposedly that is not the correct answer ? did i make an error- because i worked out the problem numerous times.
To find the maximum height reached by the rocket, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 m/s at the maximum height)
u = initial velocity (52 m/s)
a = acceleration (2.6 m/s^2)
s = displacement (maximum height)
Plugging in the values into the equation, we get:
0 = (52)^2 + 2(2.6)s
Simplifying the equation, we have:
0 = 2704 + 5.2s
Rearranging the equation to solve for s, we get:
5.2s = -2704
s = -2704 / 5.2
s ≈ -520 m
Since the height cannot be negative, we discard the negative value and the maximum height reached by the rocket is approximately 520 m.
To find the time it takes for the rocket to reach its maximum height, we can use the equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (52 m/s)
a = acceleration (2.6 m/s^2)
t = time
Plugging in the values and solving for t, we have:
0 = 52 + 2.6t
-2.6t = 52
t = -52 / -2.6
t ≈ 20 s
Therefore, the rocket reaches its maximum height after approximately 20 seconds.
To find the total time the rocket is in the air, we can double the time it takes to reach the maximum height:
Total time = 2 * time to reach maximum height
Total time = 2 * 20
Total time = 40 seconds
So, the rocket is in the air for approximately 40 seconds.