The student's question entails calculating the horizontal distance a package must be released from a drone to hit a target on the ground. The solution involves using the time it takes for the package to fall to the ground and multiplying it by the drone's horizontal velocity. The package should be released approximately 3396 meters before the target, based on the drone's elevation and horizontal speed.
The question is about projectile motion, a concept from Physics, commonly taught at the high school level. The student is asking how many horizontal meters before the target a package should be released by a drone traveling horizontally to hit the target on the ground. Since the drone is traveling at a constant horizontal speed of 120 m/s and dropping the package from a height of 4000 meters, we can solve this by using the equations of motion for freely falling objects.
We know that the acceleration due to gravity (g) is approximately 9.81 m/s2 (we can round it to 10 m/s2 for simplicity if high precision is not required). The time (t) it takes for the package to fall 4000 meters can be found by using the equation of motion h = 1/2 × g × t2, where h is the height.
First, solve for t:
- 4000 m = 1/2 × 10 m/s2 × t2
- t2 = 800 s2
- t = sqrt(800 s2)
- t ≈ 28.3 s (to the nearest tenth)
Next, calculate the horizontal distance the package travels during this time:
- Horizontal distance = speed × time
- Horizontal distance = 120 m/s × 28.3 s
- Horizontal distance ≈ 3396 m (to the nearest meter)
Therefore, the package should be released approximately 3396 meters before the target.