To find the magnitude and direction of the jet's acceleration as it comes to rest, we can use the kinematic equation which relates initial velocity \( v_i \), final velocity \( v_f \), acceleration \( a \), and distance \( d \):
\[ v_f^2 = v_i^2 + 2ad \]
Where:
- \( v_f \) is the final velocity (0 m/s, since the jet comes to rest),
- \( v_i \) is the initial velocity (71.4 m/s, due south),
- \( d \) is the distance over which the jet comes to rest (949 m),
- \( a \) is the acceleration (which we need to find).
Rearranging the equation to find \( a \):
\[ a = \frac{v_f^2 - v_i^2}{2d} \]
Substituting the known values into the equation:
\[ a = \frac{0^2 - (71.4)^2}{2 \times 949} \]
Calculating \( (71.4)^2 \):
\[ (71.4)^2 = 5097.96 \]
Now substituting back into the equation:
\[ a = \frac{-5097.96}{1898} \]
Calculating the value of \( a \):
\[ a \approx -2.68 , \text{m/s}^2 \]
The negative sign indicates the direction of the acceleration is opposite to the direction of travel of the jet. Since the jet is traveling due south, the acceleration is directed due north.
Final Answer: The magnitude of the acceleration is approximately \( 2.68 , \text{m/s}^2 \) directed due north.
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