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?
Question
Answer:
Let V = the launch velocityLet 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.
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11 months ago
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