Question

Impulse \[0.45\] is applied to a \[200\,g\] model rocket initially at rest. What will be its final speed (neglect gravity)?
A. \[2.25\,m/s\]
B. \[22.5\,m/s\]
C. \[2250\,m/s\]
D. \[4500\,m/s\]

Answer 1

Hint: Impulse is a term that quantifies the overall effect of a force acting over time. It is conventionally given the symbol \[J\] and expressed in Newton-seconds. The formula we use in the further steps is given by the impulse-momentum theorem which states that “The impulse-momentum theorem states that the impulse applied to an object will be equal to the change in its momentum”

Formulas used:
The formula of impulse is given by, \[I = mv\] (we take this because the value of initial speed is zero and hence the initial momentum will be cancelled off).

Complete step by step answer:
The following data is given in the question, mass of the model rocket, \[m = 200\,g\].The impulse applied to the rocket, \[I = 0.45\]. We know that the formula of impulse is given by \[I = mv - mu\] , but initially the model rocket is at rest so the value of the second part of the equation becomes zero.We are asked to find the value of final speed.Assigning the value of final speed to the variable \[v\].

Now bringing speed to one side in the equation, \[I = mv\]
\[v = \dfrac{I}{m}\]
We convert the value of mass of the model rocket into SI units which is conversion of grams to kilograms
\[1\,kg = 1000\,g\]
\[\Rightarrow 200\,g = \dfrac{{200}}{{10000}}kg\]
\[\Rightarrow v = \dfrac{{0.45}}{{0.200}} \\
\therefore v= 2.25\,m/s\]
Therefore, the final speed of the model rocket of mass \[200\,g\] when an impulse of \[0.45\] is applied will be \[2.25\,m/s\].

Hence, the correct answer is option A.

Note:The conversion of the mass of the model rocket from grams to kilograms is a crucial step as we have to convert the units to the SI unit of measurement. We can also use the value in grams but the value of speed wouldn’t be found in the asked unit.