The problem provides graphs representing the heights of a toy rocket (R) and a drone (D) as functions of time since they were launched. Height is measured in meters, and time is measured in seconds. The task is to analyze the graphs and describe the motion of each object in detail.

Applied MathematicsGraph AnalysisMotion AnalysisFunctionsPhysics
2025/4/24

1. Problem Description

The problem provides graphs representing the heights of a toy rocket (R) and a drone (D) as functions of time since they were launched. Height is measured in meters, and time is measured in seconds. The task is to analyze the graphs and describe the motion of each object in detail.

2. Solution Steps

Let's analyze the motion of the toy rocket (R) and the drone (D) separately.
Toy Rocket (R):
* From t=0t=0 to approximately t=2.5t=2.5 seconds, the height of the rocket increases. This means the rocket is ascending.
* At approximately t=2.5t=2.5 seconds, the rocket reaches its maximum height (around 46 meters).
* From approximately t=2.5t=2.5 seconds to t=5t=5 seconds, the height of the rocket decreases. This means the rocket is descending.
* At t=5t=5 seconds, the rocket hits the ground (height = 0).
Drone (D):
* From t=0t=0 to t=2t=2 seconds, the height of the drone increases linearly. This means the drone is rising at a constant rate.
* From t=2t=2 to t=5t=5 seconds, the height of the drone remains constant at about 22 meters. This means the drone is hovering at that altitude.
* From t=5t=5 to t=7t=7 seconds, the height of the drone decreases linearly to 0 meters. This means the drone is descending at a constant rate.
* At t=7t=7 seconds the drone reaches ground.

3. Final Answer

Toy Rocket (R): The rocket is launched upwards. It ascends for approximately 2.5 seconds, reaching a peak height of about 46 meters. Then, it descends and hits the ground at 5 seconds.
Drone (D): The drone rises at a constant rate for 2 seconds, reaching a height of 22 meters. It hovers at that height for 3 seconds (from 2 to 5 seconds). Finally, it descends to the ground linearly in 2 seconds, reaching the ground at 7 seconds.

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