Answer :
To determine 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 is the product of mass and acceleration, expressed by the formula:
[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 (m/s[tex]\(^2\)[/tex]).
Given:
- The mass ([tex]\( m \)[/tex]) of the arrow is 0.25 kg.
- The acceleration ([tex]\( a \)[/tex]) is [tex]\(196 \, \text{m/s}^2\)[/tex].
Now, substitute the given values into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
Calculating this gives:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, a force of 49 N is needed to give the arrow an acceleration of [tex]\(196 \, \text{m/s}^2\)[/tex].
[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 (m/s[tex]\(^2\)[/tex]).
Given:
- The mass ([tex]\( m \)[/tex]) of the arrow is 0.25 kg.
- The acceleration ([tex]\( a \)[/tex]) is [tex]\(196 \, \text{m/s}^2\)[/tex].
Now, substitute the given values into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
Calculating this gives:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, a force of 49 N is needed to give the arrow an acceleration of [tex]\(196 \, \text{m/s}^2\)[/tex].
