Finding Launch Speed and Maximum Height of a Toy Rocket

AI Thread Summary
The discussion focuses on calculating the launch speed and maximum height of a toy rocket that passes a window 2.2 meters high, with the window's sill at 9.0 meters above ground. The equations of motion are applied, using the height formula y=-4.9t^2+v_0t+y_0. The user attempts to derive the initial velocity (v0) and the time (t0) when the rocket reaches the window but struggles with the calculations. They realize that by manipulating the equations, they can isolate v0 and t0 to find the necessary values. The conversation emphasizes the importance of correctly applying kinematic equations to solve for the rocket's parameters.
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Homework Statement


A toy rocket moving vertically upward passes by a 2.2 m high window whose sill is 9.0m above the ground. The rocket takes 0.17s to travel the 2.2m height of the window. What was the launch speed of the rocket, and how high will it go? Assume the propellant is burned very quickly at blastoff.


Homework Equations


y=-4.9t^2+v_0t+y_0


The Attempt at a Solution


I start by assuming the rocket launched from the ground, so the initial height is 0. The height at an unknown time y(t0)=9.0=-4.9t02+v0t0, and the height .17s after is y(t0+.17)=2.2=-4.9(t0+.17)2+v0(t0+.17). If I take the difference, I end up with:
2.34161=-1.666t0+0.17v0.

If my reasoning wasn't wrong here, it seems I'm missing a piece of information to finish the problem. How would I find the exact point in time t0 where the rocket just reaches the window sill?
 
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y(t0+.17)=2.2=-4.9(t0+.17)2+v0(t0+.17).

The above equation should be

y(t0+.17)=2.2 + 9 =-4.9(t0+.17)^2+v0(t0+.17).

Now solve the equations to find vo and to.
 
I don't see how I can solve the equations. I don't know the value of t0
 
9.0=-4.9t0^2+v0t0,...(1)

2.2 + 9 =-4.9(t0+.17)^2+v0(t0+.17)...(2)

(2) - (1)

2.2 = -(4.9)[(to + .17)^2 - to^2] + vo*0.17

2.2 = -(4.9)[2*o.17*to + (0.17)^2] + vo*0.17

0.17*v0 = 2.2 + (4.9)[2*o.17*to + (0.17)^2]

Find vo and substitute is eq(1) and solve for to.
 
I didn't think of that. Thanks for the help!
 
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