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Answer :
To solve this problem, we need to use the formula for force, which is given by Newton's second law of motion. This law states that force equals mass times acceleration, often written as:
[tex]\[ F = m \times a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Given:
- The mass ([tex]\( m \)[/tex]) of the arrow is [tex]\( 0.25 \, \text{kg} \)[/tex],
- The acceleration ([tex]\( a \)[/tex]) is [tex]\( 196 \, \text{m/s}^2 \)[/tex].
Substituting these values into the formula gives:
[tex]\[ F = 0.25 \times 196 \][/tex]
Calculating this:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, the force needed to give a [tex]\( 0.25 \, \text{kg} \)[/tex] arrow an acceleration of [tex]\( 196 \, \text{m/s}^2 \)[/tex] is [tex]\( 49 \, \text{N} \)[/tex]. So, the correct answer is [tex]\( 49 \, \text{N} \)[/tex].
[tex]\[ F = m \times a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Given:
- The mass ([tex]\( m \)[/tex]) of the arrow is [tex]\( 0.25 \, \text{kg} \)[/tex],
- The acceleration ([tex]\( a \)[/tex]) is [tex]\( 196 \, \text{m/s}^2 \)[/tex].
Substituting these values into the formula gives:
[tex]\[ F = 0.25 \times 196 \][/tex]
Calculating this:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, the force needed to give a [tex]\( 0.25 \, \text{kg} \)[/tex] arrow an acceleration of [tex]\( 196 \, \text{m/s}^2 \)[/tex] is [tex]\( 49 \, \text{N} \)[/tex]. So, the correct answer is [tex]\( 49 \, \text{N} \)[/tex].
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