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Answer:
The time it takes to hit a target that is 3 feet above ground is approximately 0.35 seconds
Step-by-step explanation:
The given parameters are;
The height of the arrow above the ground = 5 ft.
The height of the target above the ground = 3 ft.
The time it takes the arrow to fall to 3 ft. from 5 ft. above the ground is given by the free fall formula, since the arrow has no vertical velocity component
The equation for free fall is h = 1/2·g·t²
Where;
h = The height of fall = 5 - 3 = 2 feet
g = The acceleration due to gravity = 32.17405 ft/s²
t = How long it takes to fall (to its target)
∴ 2 = 1/2 × 32.17405 × t²
t² = 2/(1/2 × 32.17405) ≈ 0.1243
t = √0.1243 ≈ 0.353
t = 0.35 seconds, to the nearest hundredth
Therefore, the time it takes to fall 2 ft to hit a target that is 3 feet above ground = 0.35 seconds.
The time to hit the target is simply the period the arrow gets to the target from the arch.
The time to hit the target is 0.35 seconds
The height of a parabola is calculated as:
[tex]\mathbf{h = \frac{1}{2}gt^2}[/tex]
Where:
[tex]\mathbf{h =5 - 3 = 2}[/tex] --- the difference between the height of the arrow and the height of the target.
[tex]\mathbf{g = 32.2 fts^{-2}}[/tex] --- acceleration due to gravity
So, we have:
[tex]\mathbf{2 = \frac{1}{2} \times 32.2 \times t^2}[/tex]
Multiply both sides by 2
[tex]\mathbf{4 = 32.2 \times t^2}[/tex]
Divide both sides by 32.2
[tex]\mathbf{0.124 = t^2}[/tex]
Take square roots
[tex]\mathbf{0.35 = t}[/tex]
Rewrite as:
[tex]\mathbf{t = 0.35s}[/tex]
Hence, the time to hit the target is 0.35 seconds
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