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 window

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

part b) how high will the rocket go ?

To find the launch speed of the rocket and the maximum height it will reach, we can use a few basic principles of motion and algebra.

Part a) Launch Speed of the Rocket:

Let's assume that the initial launch speed of the rocket is "v" m/s.

When the rocket reaches the window, it will have traveled a height of 2.2m.
Using the formula for vertical motion with constant acceleration:

s = ut + (1/2)at^2

Where:
s = vertical displacement (2.2m)
u = initial velocity (launch speed) of the rocket (unknown)
t = time taken to travel the height of the window (0.17s)
a = acceleration (due to gravity, which is approximately 9.8 m/s^2)

Plugging in the given values:

2.2 = v(0.17) + (1/2)(9.8)(0.17)^2

Simplifying the equation:

2.2 = 0.17v + (0.5)(9.8)(0.0289)
2.2 = 0.17v + 0.5(0.28342)
2.2 = 0.17v + 0.14171
2.2 - 0.14171 = 0.17v
2.05829 = 0.17v
v = 2.05829 / 0.17
v ≈ 12.109 m/s

Therefore, the launch speed of the rocket is approximately 12.109 m/s.

Part b) Maximum Height of the Rocket:

To find the maximum height the rocket will reach, we need to determine the time it takes for the rocket to reach its peak.

Since the rocket is moving vertically upward, it will decelerate until it eventually reaches a point where its velocity becomes zero (at its peak). The rocket will then start descending.

Using the formula for vertical motion without time:

v = u + at

At the peak of the rocket's trajectory, its final velocity (v) will be zero, meaning that the equation becomes:

0 = u + (-9.8)t

Rearranging the equation:

t = u/9.8

The time to reach the peak is the same as the time it took for the rocket to travel the height of the window, which is 0.17s.

0.17 = u / 9.8

Simplifying the equation:

u = 0.17 * 9.8
u ≈ 1.666 m/s

The initial velocity when the rocket is launched upwards is approximately 1.666 m/s.

Now, let's calculate the time it takes for the rocket to reach its maximum height using the formula for free fall motion:

v = u + at

Rearranging the equation:

t = (v - u) / a

Where:
v = final velocity (0 m/s at the peak)
u = initial velocity (1.666 m/s)
a = acceleration (-9.8 m/s^2, due to gravity)

Plugging in the values:

t = (0 - 1.666) / (-9.8)
t = 1.666 / 9.8
t ≈ 0.17 s

So, it takes the rocket approximately 0.17 seconds to reach its peak.

Now, to find the maximum height, we can use the formula for vertical motion:

s = ut + (1/2)at^2

Where:
s = vertical displacement (maximum height)
u = initial velocity (1.666 m/s)
t = time taken to reach the peak (0.17 s)
a = acceleration (-9.8 m/s^2)

Plugging in the values:

s = (1.666)(0.17) + (1/2)(-9.8)(0.17)^2

Calculating:

s ≈ 0.283 m

Therefore, the maximum height the rocket will reach is approximately 0.283 meters.