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Answer :
Certainly! Let's break down the steps needed to solve the problem:
Problem Statement:
A rocket is launched vertically with an upward acceleration of 3 m/s². Starting from the ground with an initial velocity of 0 m/s, determine how high the rocket will be after 10 seconds.
Step-by-Step Solution:
1. Identify the given parameters:
- Initial velocity ([tex]\( v_0 \)[/tex]) = 0 m/s
- Acceleration ([tex]\( a \)[/tex]) = 3 m/s²
- Time ([tex]\( t \)[/tex]) = 10 seconds
2. Select the appropriate kinematic equation:
To find the height ([tex]\( h \)[/tex]) the rocket reaches, we use the kinematic equation for displacement under constant acceleration:
[tex]\[
h = v_0 \cdot t + \frac{1}{2} \cdot a \cdot t^2
\][/tex]
In this equation:
- [tex]\( h \)[/tex] is the height,
- [tex]\( v_0 \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time,
- [tex]\( a \)[/tex] is the acceleration.
3. Substitute the known values into the equation:
[tex]\[
h = 0 \cdot 10 + \frac{1}{2} \cdot 3 \cdot 10^2
\][/tex]
4. Simplify and solve the equation:
- First, calculate [tex]\( 10^2 \)[/tex] (which is 100),
- Then multiply by the acceleration (3 m/s²),
- Finally, multiply by [tex]\(\frac{1}{2} \)[/tex].
So,
[tex]\[
h = 0 + \frac{1}{2} \cdot 3 \cdot 100
\][/tex]
[tex]\[
h = \frac{3}{2} \cdot 100
\][/tex]
[tex]\[
h = 1.5 \cdot 100
\][/tex]
[tex]\[
h = 150
\][/tex]
5. State the final result:
After calculating, we find that the height the rocket reaches after 10 seconds is 150 meters.
Therefore, the rocket will be 150 meters high after 10 seconds.
Problem Statement:
A rocket is launched vertically with an upward acceleration of 3 m/s². Starting from the ground with an initial velocity of 0 m/s, determine how high the rocket will be after 10 seconds.
Step-by-Step Solution:
1. Identify the given parameters:
- Initial velocity ([tex]\( v_0 \)[/tex]) = 0 m/s
- Acceleration ([tex]\( a \)[/tex]) = 3 m/s²
- Time ([tex]\( t \)[/tex]) = 10 seconds
2. Select the appropriate kinematic equation:
To find the height ([tex]\( h \)[/tex]) the rocket reaches, we use the kinematic equation for displacement under constant acceleration:
[tex]\[
h = v_0 \cdot t + \frac{1}{2} \cdot a \cdot t^2
\][/tex]
In this equation:
- [tex]\( h \)[/tex] is the height,
- [tex]\( v_0 \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time,
- [tex]\( a \)[/tex] is the acceleration.
3. Substitute the known values into the equation:
[tex]\[
h = 0 \cdot 10 + \frac{1}{2} \cdot 3 \cdot 10^2
\][/tex]
4. Simplify and solve the equation:
- First, calculate [tex]\( 10^2 \)[/tex] (which is 100),
- Then multiply by the acceleration (3 m/s²),
- Finally, multiply by [tex]\(\frac{1}{2} \)[/tex].
So,
[tex]\[
h = 0 + \frac{1}{2} \cdot 3 \cdot 100
\][/tex]
[tex]\[
h = \frac{3}{2} \cdot 100
\][/tex]
[tex]\[
h = 1.5 \cdot 100
\][/tex]
[tex]\[
h = 150
\][/tex]
5. State the final result:
After calculating, we find that the height the rocket reaches after 10 seconds is 150 meters.
Therefore, the rocket will be 150 meters high after 10 seconds.
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