Final answer:
To find the maximum height reached by an arrow shot upward with an initial velocity of 160 ft/s, while ignoring air resistance, you use the formula h = vo2 / (2g). This calculation yields a maximum height of 400 feet.
Step-by-step explanation:
To determine the maximum height the arrow reaches when shot straight upward with an initial velocity of 160 ft/s, we need to consider the deceleration due to gravity and the deceleration due to air resistance, which is given by v2/800. Since gravity accelerates all objects at the same rate, this deceleration is -32.2 ft/s2 on Earth. The deceleration from air resistance varies with the square of the velocity, making it necessary to solve a differential equation to find the height.
However, based on the student's prior knowledge and the specific parameters given in the question, it may be more practical to use an approximate method or kinematic equations if the effect of air resistance can be considered negligible. For high school level, we might simplify the problem by neglecting the air resistance, which would otherwise require advanced calculus. In the absence of air resistance, the maximum height can be found using the formula h = vo2 / (2g), where h is the maximum height, vo is the initial velocity and g is the acceleration due to gravity. Using this formula, the maximum height can be calculated as follows:
h = (160 ft/s)2 / (2 * 32.2 ft/s2)
h = 400 ft
Therefore, if we ignore air resistance, the arrow would reach a maximum height of 400 feet before starting to fall back to the ground.