Understanding Motion from Graphs


Launching a Rocket When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands.


The figure here shows velocity data from the flight of the model rocket. Use the data to answer the following.


c. When did the rocket reach its highest point? What was its velocity then?

Verified step by step guidance

1. Observe the graph provided, which plots velocity (in ft/sec) against time (in seconds) for the rocket's flight.
2. Identify the point on the graph where the velocity is zero, as this indicates the highest point of the rocket's flight. This is because the rocket stops ascending and starts descending at this point.
3. Notice that the velocity becomes zero at approximately 5 seconds after launch, which is when the rocket reaches its highest point.
4. At the highest point, the velocity of the rocket is 0 ft/sec, as indicated by the graph where the curve crosses the horizontal axis.
5. Understand that after reaching the highest point, the rocket begins to fall, and the velocity becomes negative, indicating downward motion.

Key Concepts

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both speed and direction. In the context of the rocket's flight, the velocity graph shows how the rocket's speed changes over time, indicating periods of acceleration, coasting, and descent.

Critical Points

Critical points occur where the derivative of a function is zero or undefined, indicating potential maxima, minima, or points of inflection. In the case of the rocket's velocity graph, the highest point of the rocket's flight corresponds to a critical point where the velocity transitions from positive to negative, marking the peak altitude.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of data to extract meaningful information. For the rocket's velocity graph, understanding the shape and key features, such as peaks and troughs, allows us to determine when the rocket reached its highest point and the corresponding velocity at that moment.