Question

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?

Answer 1

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.

Answer: Arrow b arrives first.