Final answer:
The shape of the graph of h(t) reflects changes in the astronauts' speed over time. It can be a straight line, a parabola, or a sinusoidal function depending on the nature of the function.
Step-by-step explanation:
The shape of the graph of h(t) can reflect changes in the astronauts' speed over time depending on the nature of the function. Here are a few examples of different shapes:
- If h(t) is a linear function, such as h(t) = 2t, the graph would be a straight line with a constant slope. This would indicate a constant speed.
- If h(t) is a quadratic function, such as h(t) = t^2, the graph would be a parabola. The steepness of the parabola would indicate changes in speed. A steeper slope at a particular point on the graph would correspond to a higher speed at that time.
- If h(t) is a sinusoidal function, such as h(t) = sin(t), the graph would have a repetitive pattern. The amplitude of the sine wave would correspond to the magnitude of speed, with higher amplitude indicating higher speed.