To find the distance the arrow traveled, we calculate the initial velocity using the work done by the bowstring, determine the time of flight using vertical motion equations, and then multiply by the initial horizontal velocity to find the horizontal distance.
To calculate how far the arrow landed from the archer, we must first determine the initial velocity of the arrow using the work-energy theorem, which states that the work done by the force of the bow is equal to the kinetic energy of the arrow just after it is released. The work done on the arrow by the archer is Work = Force × displacement = 390 N × 0.75 m = 292.5 J. Assuming that there are no energy losses, this work is converted directly into the kinetic energy of the arrow: Kinetic Energy = (1/2)mv² = 292.5 J, which allows us to solve for the initial velocity v.
Next, using the equation of projectile motion and the fact that the horizontal velocity remains constant since we are ignoring air resistance, we calculate the time of flight based solely on the vertical motion. The time it takes for the arrow to fall from a height of 1.10 m can be found by using the kinematic equation: 1.10m = (1/2)gt², where g is the acceleration due to gravity (9.8 m/s²).
Finally, multiplying the time of flight by the horizontal component of the initial velocity gives us the horizontal distance the arrow traveled before hitting the ground. This calculated distance will correspond to one of the choices provided: a) 8 m b) 10 m c) 16 m d) 20 m.