Answer :

To find the force needed to give a 0.25 kg arrow an acceleration of [tex]\(196 \, \text{m/s}^2\)[/tex], we can use Newton's Second Law of Motion. This law states that force can be calculated by multiplying mass and acceleration. The formula is:

[tex]\[ F = m \times a \][/tex]

where:
- [tex]\( F \)[/tex] is the force (in newtons, N),
- [tex]\( m \)[/tex] is the mass (in kilograms, kg),
- [tex]\( a \)[/tex] is the acceleration (in meters per second squared, [tex]\( \text{m/s}^2 \)[/tex]).

Let's plug in the numbers given in the problem:

1. The mass [tex]\( m \)[/tex] of the arrow is [tex]\( 0.25 \, \text{kg} \)[/tex].
2. The acceleration [tex]\( a \)[/tex] is [tex]\( 196 \, \text{m/s}^2 \)[/tex].

Now, calculate the force:

[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]

Upon doing this multiplication, we find that:

[tex]\[ F = 49 \, \text{N} \][/tex]

Therefore, a force of [tex]\(\textbf{49 N}\)[/tex] is needed to give the arrow the specified acceleration.

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