- #1
David112234
- 105
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Homework Statement
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During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 990 m above the earth's surface. The rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance.
What it asks for : What must be the value of T in order for the rocket to reach the required altitude?
Homework Equations
basic kinematics formulas
X= Xo + VoT+1/2AT^2
V=Vo+AT
V^2=Vo^2+2A(X-Xo)
o denotes initial
The Attempt at a Solution
| X3= 990 V3=0
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| X2= V2= A=-9.8
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| X1=0 V1=0 A=16.0 m/s
X3=X2+V2T-1/2 9.8T^2
X2=X1+V1T+.5*16*T^2
X2=0+0T+.5^16*T^2
X2=8T^2
plugging pack into original equation:
X3=8T^2 +V2T -4,9 T^2
combining like terms
X3= 3.1T^2 + V2T
finding V2:
V2=V1+16T
V2=0+16T
V2=16T
plugging back in
X3= 3.1T^2 + 16T
X3=990
990=3.1T^2 + 16T
it is a quadratic equation I graphed it to find the X value, I got 20.65 , but it is wrong, where Did I go wrong?