Amodel rocket rises with constant acceleration to a height of 4.2 m, at which point its speed is 27.0 m/s. how much time does it take for the rocket to reach this height? what was the magnitude of the rocket's acceleration? find the height of the rocket 0.20 s after launch. find the speed of the rocket 0.20 s after launch.

Answers:

a)

b)

c)

d)

Explanation:

For this situation we will use the following equations:

(1)  

(2)  

Where:  

is the height of the model rocket at a given time

is the initial height of the model rocket

is the initial velocity of the model rocket since it started from rest

is the velocity of the rocket at a given height and time

is the time it takes to the model rocket to reach a certain height

is the constant acceleration due gravity and the rocket's thrust

The average velocity of a body moving at a constant acceleration is:

(3)

For this rocket is:

(4)

Time is determined by:

(5)

(6)

Hence:

(7)

Using equation (1), with initial height and velocity equal to zero:

(8)  

We will use :

(9)  

Finding :

(10)  

Using again but for :

(11)

(12)

We will use equation (2) remembering the rocket startted from rest:

(13)  

(14)  

Finally:

(15)  

we need to know the time interval during which the force acts. impulse of force = momentum change