An arrow was shot horizontally at a speed of 40 m/s from a bow held 1.5 meters above the ground. It misses the target and hits the ground. How much time does it take the arrow to hit the ground?

If we can ignore any effects of air resistance ... and we always do ... then it makes no difference what its horizontal speed was, or whether it had any at all. It hits the ground in the same time as an arrow that just dropped from the bow to ground.
The distance an object falls from rest in ' T ' seconds, on account of gravity, is
D = 1/2 G T² . ('G' is the acceleration of gravity, 9.8m/s² )
This arrow falls 1.5 meters,and 1/2 G is 9.8/2 = 4.9 m/s² .
1.5 m = 4.9 m/s² T²
Divide each side by 4.9 m/s² : (1.5 / 4.9) sec² = T²
Take the square root of each side: T = square root of (1.5/4.9) = 0.553 sec

Answered by AL2006 | 2024-06-10

To determine how long it takes for an arrow shot horizontally to hit the ground, we can ignore the horizontal motion since it does not affect the time of flight. The arrow's vertical motion is influenced by gravity alone. Using the equation for the time of fall under gravity, we have:
t = √(2h/g),
where:
t is the time in seconds,
h is the height in meters (1.5 m),
g is the acceleration due to gravity (approximately 9.8 m/s2).
Plugging in the values, we get:
t = √(2 × 1.5 m / 9.8 m/s2)
t = √(3 / 9.8)
t = √(0.30612244898)
t ≈ 0.5534 seconds (rounded to four decimal places)
Therefore, it takes approximately 0.55 seconds for the arrow to hit the ground.

Answered by ChristopherEdwin | 2024-06-18

The arrow takes approximately 0.553 seconds to hit the ground after being shot horizontally from a height of 1.5 meters. This time is calculated using the formula for the distance fallen under gravity. The horizontal speed does not affect the time it takes to hit the ground.
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Answered by AL2006 | 2024-09-26