The impulse $J$ applied to an object is given by the formula:

$J = F \cdot \Delta t$

where:

• $F$ is the force applied, and
• $\Delta t$ is the time duration over which the force is applied.

In this case:

• $F = 12,000 \, \text{N}$
• $\Delta t = 0.70 \times 10^{-3} \, \text{s} = 0.0007 \, \text{s}$

Substitute these values into the formula:

$J = 12,000 \, \text{N} \cdot 0.0007 \, \text{s}$

Calculating this:

$J = 8.4 \, \text{N}\cdot\text{s}$

Thus, the magnitude of the impulse on the ball is $\mathbf{8.4 \, N \cdot s}$.

Would you like to go over any details or have questions about this calculation?

Here are some related questions:

1. How does impulse relate to a change in momentum?
2. If the force was applied for a longer time, how would it affect the impulse?
3. What is the relationship between impulse and average force?
4. How does this impulse impact the ball's velocity if mass is known?
5. What is the difference between impulse and force in terms of effect on the ball?

Tip: Remember, impulse is a vector quantity, so it has both magnitude and direction!