Answered

Discover a wealth of knowledge and get your questions answered on IDNLearn.com. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

The Rocket Club is planning to launch a pair of model rockets. To build the rocket, the club needs a rocket body paired with an engine. The table lists the mass of three possible rocket bodies and the force generated by three possible engines.

\begin{tabular}{|c|c|c|c|}
\hline
Body & Mass (kg) & Engine & Force (N) \\
\hline
1 & 0.500 & 1 & 25 \\
\hline
2 & 1.5 & 2 & 20 \\
\hline
3 & 0.750 & 3 & 30 \\
\hline
\end{tabular}

Based on Newton's laws of motion, which combination of rocket bodies and engines will result in the acceleration of [tex]$40 \, m/s^2$[/tex] at the start of the launch?

A. Body 3 + Engine 1
B. Body 2 + Engine 2
C. Body 1 + Engine 2
D. Body 1 + Engine 1

Sagot :

GinnyAnsweridn
To find which combinations of rocket bodies and engines will result in an acceleration of [tex]\( 40 \, m/s² \)[/tex], we must use Newton's second law of motion which states [tex]\( F = ma \)[/tex]. Rearranging this equation to solve for acceleration [tex]\( a \)[/tex], we get:

[tex]\[ a = \frac{F}{m} \][/tex]

We will calculate the acceleration for each combination of rocket bodies and engines and find which one results in an acceleration of [tex]\( 40 \, m/s² \)[/tex].

1. Body 1 + Engine 1
- Mass ([tex]\( m \)[/tex]) = 0.500 kg
- Force ([tex]\( F \)[/tex]) = 25 N

[tex]\[ a = \frac{25 \, \text{N}}{0.500 \, \text{kg}} = 50 \, m/s² \][/tex]

2. Body 2 + Engine 2
- Mass ([tex]\( m \)[/tex]) = 1.5 kg
- Force ([tex]\( F \)[/tex]) = 20 N

[tex]\[ a = \frac{20 \, \text{N}}{1.5 \, \text{kg}} = 13.33 \, m/s² \][/tex]

3. Body 3 + Engine 3
- Mass ([tex]\( m \)[/tex]) = 0.750 kg
- Force ([tex]\( F \)[/tex]) = 30 N

[tex]\[ a = \frac{30 \, \text{N}}{0.750 \, \text{kg}} = 40 \, m/s² \][/tex]

4. Body 1 + Engine 2
- Mass ([tex]\( m \)[/tex]) = 0.500 kg
- Force ([tex]\( F \)[/tex]) = 20 N

[tex]\[ a = \frac{20 \, \text{N}}{0.500 \, \text{kg}} = 40 \, m/s² \][/tex]

5. Body 2 + Engine 1
- Mass ([tex]\( m \)[/tex]) = 1.5 kg
- Force ([tex]\( F \)[/tex]) = 25 N

[tex]\[ a = \frac{25 \, \text{N}}{1.5 \, \text{kg}} = 16.67 \, m/s² \][/tex]

6. Body 3 + Engine 1
- Mass ([tex]\( m \)[/tex]) = 0.750 kg
- Force ([tex]\( F \)[/tex]) = 25 N

[tex]\[ a = \frac{25 \, \text{N}}{0.750 \, \text{kg}} = 33.33 \, m/s² \][/tex]

7. Body 1 + Engine 3
- Mass ([tex]\( m \)[/tex]) = 0.500 kg
- Force ([tex]\( F \)[/tex]) = 30 N

[tex]\[ a = \frac{30 \, \text{N}}{0.500 \, \text{kg}} = 60 \, m/s² \][/tex]

8. Body 2 + Engine 3
- Mass ([tex]\( m \)[/tex]) = 1.5 kg
- Force ([tex]\( F \)[/tex]) = 30 N

[tex]\[ a = \frac{30 \, \text{N}}{1.5 \, \text{kg}} = 20 \, m/s² \][/tex]

9. Body 3 + Engine 2
- Mass ([tex]\( m \)[/tex]) = 0.750 kg
- Force ([tex]\( F \)[/tex]) = 20 N

[tex]\[ a = \frac{20 \, \text{N}}{0.750 \, \text{kg}} = 26.67 \, m/s² \][/tex]

From these calculations, we find that the combinations resulting in an acceleration of [tex]\( 40 \, m/s² \)[/tex] are:

- Body 1 + Engine 2
- Body 3 + Engine 3

Therefore, the combinations that will achieve the required acceleration are [tex]\( \boxed{\text{Body 1 + Engine 2 and Body 3 + Engine 3}} \)[/tex].
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.