Answer: the average vertical component of velocity between the object's release and its striking the ground is 49.5 m/s or 178 km/h
Explanation:
1) The motion of an object under the action of gravity, when air resistance is neglected is called projectile motion. The path is a curve with the form of a parabola.
2) The equations that rule that motion are:
- Horizontal speed:
- Vx = Vox = constant.
- In this case it is the same horizontal speed of the plane at the moment when the object was proyected. Vx = 429 km/h.
Vy = Voy + gt
d = yo - Voy×t - gt² / 2
Vy² = Voy² - 2gd
- Since, you know Voy =0, g = 9.81 m/s², and d = 500m, you can use the last equation, leading to:
Vy² = 2(9.81m/s²)(500m) = 9,810 m²/s² ⇒ Vy = √(9,810 m²/s²) = 99 m/s
3) As per definition the average velocity is displacement / time, so you need to find the time to reach the ground.
- You can use the formula Vy = Voy + gt
- Clear t: t = (Vy - Voy) / g = (99 m/s - 0) / 9.81 m/s = 10.1s
- Average vertical velocity = 500 m / 10.1s = 49.5 m/s.
- You can convert to km/h: 49.5 m/s × 1km/1,000m × 3600s/h = 178 km/h
4) Conclusion: the average vertical component of velocity between the object's release and its striking the ground is 49.5 m/s or 178 km/h
