A model rocket is launched vertically upward from the ground. After 4.3s, its fuel is completely burned. Assume uniform acceleration of 3.0 m/s2 while the fuel is burning. What is the velocity of the rocket at the instant that the fuel is completely burned? What's the rocket's maximum displacement during its motion?
To find the velocity of the rocket at the instant the fuel is burned, we can use the formula for velocity:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 0 m/s (since the rocket is initially at rest)
a = 3.0 m/s^2
t = 4.3 s
Plugging these values into the formula:
v = 0 + (3.0)(4.3)
v = 0 + 12.9
v = 12.9 m/s
So, the velocity of the rocket when the fuel is completely burned is 12.9 m/s.
To find the maximum displacement of the rocket during its motion, we can use the formula for displacement:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity
t = time
a = acceleration
First, let's find the displacement during the burning of the fuel. During this time, the rocket has uniform acceleration, so we can use the same formula:
s1 = (1/2)at^2
Plugging in the given values:
s1 = (1/2)(3.0)(4.3)^2
s1 = (1/2)(3.0)(18.49)
s1 = 27.735 m
Now, let's find the displacement after the fuel is burned. Since the fuel is burned, there is no more acceleration, and the rocket's velocity remains constant at 12.9 m/s.
s2 = ut
s2 = (12.9)(4.3)
s2 = 55.47 m
To find the maximum displacement, we add the two displacements together:
s = s1 + s2
s = 27.735 + 55.47
s = 83.205 m
So, the rocket's maximum displacement during its motion is 83.205 m.