Final answer:
The arrow is in the air for a time equal to the range divided by the initial velocity. The range of the arrow is equal to the initial velocity. Projectile motion equations are used to solve for these values.
Step-by-step explanation:
To determine how long the arrow is in the air, we can use the equation: time = distance / velocity. Since the arrow is fired horizontally, the distance is the range, and the velocity is the horizontal component of the initial velocity, which is 70.6 m/s. Therefore, the time of flight is: time = range / velocity = range / 70.6.
To find the range of the arrow, we can use the equation for horizontal motion: range = velocity × time. Plugging in the values, we have: range = 70.6 × time.
Substituting the expression for time from the first equation into the second equation, we get: range = 70.6 × (range / 70.6). Simplifying, we find that the range is equal to the initial velocity, which is 70.6 meters.