a toy rocket moving vertically upward passes by a 2.2m- high window whose sill is 7.0m above the ground. the rocket takes 0.17s to travel the 2.2m height of the wondow

part a): what was the launch speed of the rocket ? assume the propellant is burned very quickly at blastoff

part b) how high will the rocket go ?

where did that 22.2 come from?

v(o) = 2• h(o) /t +gt/2 = 2.2/0.17 + 9.8•0.17/2 = 25.047 m/s.

22.2 was a typo error of 2*2.2, but the result was ok.

thats wrong, no 2* h(o)

To solve this problem, we can use the kinematic equations of motion, specifically the equation for vertical motion:

y = yo + vot - (1/2)gt^2

where:
- y is the displacement or height traveled (in this case, 2.2m),
- yo is the initial height (in this case, 0m since the rocket starts from the ground),
- vo is the initial velocity (launch speed) we need to find,
- g is the acceleration due to gravity (-9.8 m/s^2), and
- t is the time taken to travel a certain height (in this case, 0.17s).

Part a) Finding the launch speed:
Solving for vo in the equation, we get:

y = yo + vot - (1/2)gt^2
2.2 = 0 + vo(0.17) - (1/2)(9.8)(0.17^2)

Simplifying further:

2.2 = 0.17vo - 0.0421
2.2 + 0.0421 = 0.17vo
2.2421 = 0.17vo
vo = 2.2421/0.17

Using a calculator, we find that the launch speed of the rocket is approximately 13.171 m/s.

Part b) Finding the maximum height reached by the rocket:
To find the maximum height, we need to calculate the time it takes for the rocket to reach its highest point and then use the equation y = yo + vot - (1/2)gt^2.

At the highest point, the vertical velocity of the rocket becomes zero. This means the time taken to reach the maximum height is half of the total time taken to travel the initial height of 2.2m (0.17s).

Thus, the time taken to reach the maximum height is 0.17s / 2 = 0.085s.

Now we can calculate the maximum height y using the equation:

y = yo + vot - (1/2)gt^2
y = 0 + vo(0.085) - (1/2)(9.8)(0.085^2)

Substituting the value of vo (13.171 m/s) and solving:

y = 0 + 13.171(0.085) - (1/2)(9.8)(0.085^2)

Using a calculator, we find that the maximum height reached by the rocket is approximately 1.109 meters.

Let’s find the initial velocity of rocket.

Since
h(o) = v(o)•t - g•t^2/2,
v(o) = 2• h(o) /t +gt/2 = 22.2/0.17 + 9.8•0.17/2 = 25.047 m/s.
Now let’s find the time of reaching the max height
0 = v(o) - g•t1
t1 = v(o)/g = 25.047/9.8 = 2.56 s.
The max height (from the sill)
h1 = v(o)•t1-gt1^2/2 = 25.047•2.56 =9.8•(2.56)^2/2 = 96.13 m.
The max height (from the ground) is
H = 96.13 + 7 = 103.13 m.
H = gt2^2/2 .
t2= sqrt(2•H/g) = sqrt(2•103.13/9.8) = 4.59 s.
v =g•t2 = 9.8•4.59 = 44.96 m/s