A 4.40 kg model rocket is launched, shooting 53.0 g of burned fuel from its exhaust at an average velocity of 650 m/s. What is the velocity of the rocket
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Answer:
Given data:
Mass of the model rocket,
m
1
=
4.40
k
g
m1=4.40 kg
Mass of the fuel,
m
2
=
53.0
g
=
0.053
k
g
m2=53.0 g=0.053 kg
Average velocity of the exhaust gases,
v
2
=
650
m
/
s
v2=650 m/s
Let the velocity of the rocket be
v
1
.
v1.
From the conservation law of the linear momentum, the change in momentum must be equal to zero.
Thus,
m
1
v
1
+
m
2
v
2
=
0
m1v1+m2v2=0
Here, we have assumed that the velocity along the forward direction as positive.
Plugging in values,
4.40
×
v
1
+
0.053
×
(
−
650
)
=
0
4.40×v1+0.053×(−650)=0
On solving,
v
1
=
7.82
m
/
s
.
v1=7.82 m/s.
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