Two arrows are launched at the same time with the same speed. arrow a at an angle greater than 45 degrees, and arrow b at an angle less than 45 degrees. both land at the same spot on the ground. which arrow arrives first?
Accepted Solution
A:
Let V = the launch velocity Let θ = the launch angle Let d = the horizontal distance traveled
Ignore air resistance.
The horizontal component of velocity is u = V cos θ The time of flight is t = d/(V cosθ) = (d/V) secθ
Create a table of θ versus t as shown below. θ t/(d/V) ---- ---------- 45 1.4142 40 1.3054 35 1.2208 30 1.1547
The graph shows that as the launch angle decreases below 45°, the time of flight decreases. Therefore arrow b (θ < 45°) arrives first.