According to the given data, the time that the arrow spends in the air is 6.70 seconds, and the time someone has to drop the apple after the arrow is shot, so that the arrow hits the apple, is 5.60 seconds.
<h3>Further explanation</h3>
Part 1. First let's focus on the first question. This is a 2D problem (since the arrow moves in 2 directions), therefor we can write equations for both dimensions in which the arrow moves. Let's call <em>x</em> the distance travelled by the arrow on the horizontal direction and <em>y</em> the distance travelled by the arrow on the vertical direction.
Lets suppose that the arrow was shot from a point which we will call the origin (meaning zero horizontal and vertical displacement), and let's call <em>ta </em>the time spent by the arrow on the air. The equations of motion for the arrow will be:
Where <em>V</em> is the initial speed of the arrow. If we evaluate both of the above expressions at <em>ta</em>, we know that its horizontal displacement is 220 m, and its vertical displacement is 0 m. Therefor:
Therefor we have a system of 2 unknowns (<em>V</em> and <em>ta</em>) and 2 equations. Solving for <em>V</em> from the first equation and substituting on the second we find that:
Solving for <em>ta</em> we find that:
Plugging in numerical values, we get that <em>ta</em> is 6.70 seconds.
Part 2. To know the exact moment at which we need to drop the apple so that the arrow hits it, we need to compute that time it takes to fall those 6 meters. Since the apple is dropped with zero initial speed, we can find the time it takes to fall as:
Which is around 1.10 seconds. Therefor we need to drop the apple 5.60 seconds after the arrow is shot.
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<h3>Keywords</h3>
Free falling objects, projectile, gravity