A model rocket is launched straight upward
with an initial speed of 47.9 m/s. It acceler-
ates with a constant upward acceleration of
2.40 m/s2 until its engines stop at an altitude
of 190 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
When does the rocket reach maximum height?
How long is the rocket in the air?
Can someone please help. What should i do.
with an initial speed of 47.9 m/s. It acceler-
ates with a constant upward acceleration of
2.40 m/s2 until its engines stop at an altitude
of 190 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
When does the rocket reach maximum height?
How long is the rocket in the air?
Can someone please help. What should i do.
-
Alright this involves a lot of equations.
The first being: 2(Xf)a + (Vi)^2 = (Vf)^2
You use this equation to find your final velocity. You need your final velocity to find out the time it took for the rocket to reach an altitude of 190m
So plug stuff in... 2(190)(2.4)+ 47.9^2 = (Vf)^2
Vf = 56.6
Okay now we need time. So let's use this equation: Vi + at = Vf
47.9 + 2.4t = 56.6
t = 3.625
So 3.625 seconds is how long it took for the rocket to reach 160m.
Now at 160m the engines are cut off, so now the rocket is experiencing an acceleration of -9.81 (that of gravity).
To find maximum height we need to find when the V = 0
So let's use a familiar equation.
Vi + at = Vf
This time Vi is the V at 160m... So it is 56.6
a is like I said that of gravity, and Vf is 0 because that is when the rocket stops moving up and is now changing it's velocity to move down. (If you do not understand why V = 0, ask me!)
0= 56.6 + (-9.81)t
t = 5.77
So 5.78 seconds after the rocket reaches 160m, it reaches it's maximum height.
Now to find maximum height we use the equation:
Xf = Xi + (Vi)t + 1/2at^2
Because we are finding the max height from when the engine cuts off, we use these numbers
Xi = 160
Vi = 56.6
a = -9.81
t = 5.77
So let's plug it in...
Xf = 160 + 56.6 (5.77) + (-9.8/2)(5.77)^2
Xf = 323.45
This is your maximum height.
Now this is the easy part.
You know that the rocket takes 9.395 seconds to get to it's maximum height.
(The time it takes to get to 160m + the time it take to get to max height from 160m) = 3.625 + 5.77 = time to get to max height
Now find the time it take the rocket to get back to the ground.
Use: Xf = Xi + (Vi)t + 1/2at^2
Xf = 0
Xi = 323.45
Vi = 0 (because we are finding t from max height wher v is 0)
a = -9.81
0 = 323.45 + 0 + (-9.8/2)t^2
t = 8.12
So add the time it takes for the rocket to fall, to the time it takes for the rocket to reach it's maximum height.
8.12 + 9.395 = 17.52 seconds spent in the air.
The first being: 2(Xf)a + (Vi)^2 = (Vf)^2
You use this equation to find your final velocity. You need your final velocity to find out the time it took for the rocket to reach an altitude of 190m
So plug stuff in... 2(190)(2.4)+ 47.9^2 = (Vf)^2
Vf = 56.6
Okay now we need time. So let's use this equation: Vi + at = Vf
47.9 + 2.4t = 56.6
t = 3.625
So 3.625 seconds is how long it took for the rocket to reach 160m.
Now at 160m the engines are cut off, so now the rocket is experiencing an acceleration of -9.81 (that of gravity).
To find maximum height we need to find when the V = 0
So let's use a familiar equation.
Vi + at = Vf
This time Vi is the V at 160m... So it is 56.6
a is like I said that of gravity, and Vf is 0 because that is when the rocket stops moving up and is now changing it's velocity to move down. (If you do not understand why V = 0, ask me!)
0= 56.6 + (-9.81)t
t = 5.77
So 5.78 seconds after the rocket reaches 160m, it reaches it's maximum height.
Now to find maximum height we use the equation:
Xf = Xi + (Vi)t + 1/2at^2
Because we are finding the max height from when the engine cuts off, we use these numbers
Xi = 160
Vi = 56.6
a = -9.81
t = 5.77
So let's plug it in...
Xf = 160 + 56.6 (5.77) + (-9.8/2)(5.77)^2
Xf = 323.45
This is your maximum height.
Now this is the easy part.
You know that the rocket takes 9.395 seconds to get to it's maximum height.
(The time it takes to get to 160m + the time it take to get to max height from 160m) = 3.625 + 5.77 = time to get to max height
Now find the time it take the rocket to get back to the ground.
Use: Xf = Xi + (Vi)t + 1/2at^2
Xf = 0
Xi = 323.45
Vi = 0 (because we are finding t from max height wher v is 0)
a = -9.81
0 = 323.45 + 0 + (-9.8/2)t^2
t = 8.12
So add the time it takes for the rocket to fall, to the time it takes for the rocket to reach it's maximum height.
8.12 + 9.395 = 17.52 seconds spent in the air.