Final answer:
To calculate how far the arrow landed from the archer, we need to first calculate the initial velocity of the arrow using the work done by the force exerted on the string and then apply projectile motion to find out the horizontal distance covered.
Step-by-step explanation:
To solve how far the arrow landed from the archer, we have to calculate the initial velocity of the arrow using the work-energy principle and then apply the principles of projectile motion.
Step 1: Calculating Initial Velocity
We assume that the force exerted on the bowstring behaves like a spring force. The work done on the arrow can be calculated by the formula Work = Force × Distance, which will be equal to the kinetic energy of the arrow when it leaves the bow. The kinetic energy (KE) can be expressed as KE = 0.5 × Mass × Velocity^2. From the question we have:
Force (F) = 390 N
Distance (d) = 0.75 m
Mass (m) = 0.20 kg
So, the initial velocity (v) of the arrow is found using the equation:
0.5 × m × v^2 = F × d
Step 2: Calculating Distance
Once we have the initial velocity, we can then calculate the time it takes for the arrow to fall to the ground from a height of 1.10 m, ignoring air resistance, by using the equation for free fall. After finding the time, we multiply it by the initial horizontal velocity to find out how far the arrow lands.
The distance the arrow travels horizontally is:
Distance = Initial Velocity × Time