Answer :
The recoil speed of the archer is 2.07 m/s in the opposite direction of the arrow. This can be calculated using the conservation of momentum.
Momentum is defined as mass multiplied by velocity and is conserved during collisions.
The initial momentum of the archer-arrow system is 77.11 kg x 98.89 m/s = 7,624.14 kg m/s.
Since the arrow has a mass of 101 g, its velocity after the shot is 0 m/s, resulting in a final momentum of 7,523.14 kg m/s.
Since the total momentum is conserved, the velocity of the archer must be equal to the difference between the initial and final momentum divided by the mass of the archer: (7,624.14 - 7,523.14) / 77.11 = 2.07 m/s.
Therefore, the recoil speed of the archer is 2.07 m/s.
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