14. A hunter aims directly at a target (on the same level)38.0 m away.(a) If the arrow leaves the bow at a speed of 23.1m/s by how much will it miss the target? (b) At what angle should the bow be aimed so the target will be hit?

(a) To find out by how much the arrow will miss the target, we need to calculate the horizontal distance covered by the arrow. Since the arrow is aimed directly at the target, the vertical displacement is zero, and the horizontal displacement is equal to the horizontal component of the arrow's velocity multiplied by the time it takes to reach the target.The horizontal component of the arrow's velocity can be calculated using the formula: where is the initial velocity of the arrow and is the angle at which the bow should be aimed.Since the arrow is aimed directly at the target, the angle is , and the cosine of is . Therefore, the horizontal component of the arrow's velocity is: The time it takes for the arrow to reach the target can be calculated using the formula: where is the distance to the target.Substituting the given values, we have: Now, we can calculate the horizontal distance covered by the arrow: Therefore, the arrow will miss the target by approximately .(b) To find the angle at which the bow should be aimed so that the target will be hit, we need to calculate the angle at which the arrow's trajectory intersects the target.The vertical component of the arrow's velocity can be calculated using the formula: where is the initial velocity of the arrow and is the angle at which the bow should be aimed.We can use the equation of motion for vertical displacement: where is the vertical displacement and is the acceleration due to gravity.We want to find the angle such that the vertical displacement is equal to the height of the target. Let's assume the height of the target is .Substituting the given values, we have: We need to solve this equation for . This can be done numerically or using a calculator with trigonometric functions.After solving for , we find that the angle at which the bow should be aimed is approximately .