To determine the height at which the arrow is moving with a speed of 8 m/s, we can use the principles of projectile motion. Since the arrow is shot straight up, we only need to consider the vertical motion.
Let's denote:
- u as the initial velocity (15 m/s)
- v as the final velocity (8 m/s)
- g as the acceleration due to gravity (-9.8 m/s², taking into account its downward direction)
- h as the height we want to find
Using the equation for the final velocity in vertical motion: v² = u² + 2gh
Rearranging the equation to solve for h: h = (v² - u²) / (2g)
Plugging in the given values: h = (8² - 15²) / (2 * -9.8)
Calculating the expression: h = (64 - 225) / (-19.6) h = -161 / -19.6 h ≈ 8.22 meters
Therefore, when the arrow is moving with a speed of 8 m/s, it is at a height of approximately 8.22 meters above the initial launch point.