Answer:
The force the archer need to pull in order to achieve the height is approximately 101.8 N
Step-by-step explanation:
By energy conservation principle, puling an elastic bow with a force, for a given distance, performs work which is converted to the potential energy of the arrow at height
The given parameters are;
The mass of the arrow, m = 45.0 grams = 0.045 kg
The distance the elastic bow is pulled, d = 65.0 cm = 0.65 m
The height at which the arrow is reaches, h = 150.0 meters
Let 'F', represent the force the archer need to pull in order to achieve the height
Work done, W = Force × Distance moved in the direction of the force
Therefore;
The work done in pulling the arrow, W = F × d
By energy conservation, we have;
The work done in pulling the arrow, W = The potential energy gained by the arrow, P.E.
W = P.E.
The potential energy gained by the arrow, P.E. = m·g·h
Where;
m = The mass of the arrow
g = The acceleration due to gravity = 9.8 m/s²
h = The height the arrow reaches
∴ by plugging in the values, P.E. = 0.045 kg ×9.8 m/s² × 150 m = 66.15 J
W = F × d = F × 0.065 m
Also, W = P.E. = 66.15 J
∴ W = F × 0.065 m = 66.15 J
F × 0.065 m = 66.15 J
F = 66.15 J/(0.65 m) = 1323/13 N ≈ 101.8 N
The force the archer need to pull in order to achieve the height, F ≈ 101.8 N.