To find the force required to bring the object to rest, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma).
First, we need to calculate the acceleration (a) of the object. We know the initial velocity (v_i) and the final velocity (v_f), as well as the time (t) taken to come to rest.
- Initial velocity (v_i) = 133.0 m/s (the velocity just before impact).
- Final velocity (v_f) = 0 m/s (the object is brought to rest).
- Time (t) = 2.5 seconds.
The acceleration can be calculated using the formula:
\[ a = \frac{v_f - v_i}{t} \]
Substituting in the values:
\[ a = \frac{0 , \text{m/s} - 133.0 , \text{m/s}}{2.5 , \text{s}} = \frac{-133.0 , \text{m/s}}{2.5 , \text{s}} = -53.2 , \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity (which makes sense, as the object is slowing down).
Now we can calculate the force (F) using the mass (m) and the acceleration (a):
\[ F = m \cdot a \]
Substituting in the values:
\[ F = 56.0 , \text{kg} \cdot (-53.2 , \text{m/s}^2) = -2979.2 , \text{N} \]
The negative sign indicates that the force is acting in the opposite direction of the object's motion (which is expected as it is a stopping force).
Thus, the magnitude of the force required to bring the object to rest is:
\[ F \approx 2979.2 , \text{N} \]
In conclusion, the force required to bring the object to rest is approximately 2979.2 N in the direction opposite to the motion.