An astronaut stands on the surface of a spherical asteroid that has a weak gravitational field but no atmosphere. The astronaut throws a small rock straight upward, as shown at left above. The rock travels upward until it reaches a distance of 2R from the center of the asteroid, where R is the asteroid’s radius, and then falls back down to the asteroid’s surface. The graph at left below shows the rock’s velocity as a function of time after being thrown upward with an initial velocity v01. The dashed line shows what the velocity would be if the rock experienced a constant acceleration, and the solid curve shows the rock’s actual velocity.

After the rock lands back on the surface, the astronaut then throws the rock straight upward a second time but with a greater force so that the rock’s initial speed v02 is greater than initial speed v01 for the first throw. The graph at right below shows the rock’s velocity as a function of time after being thrown upward the second time.
In a clear, coherent, paragraph-length response that may also contain equations and/or drawings (if you would like to submit a drawing, draw it on a separate piece of paper and turn it in to your teacher), make claims for the following aspects of the rock’s motion.

For the first throw, state a claim for what is happening at time t1.
State a claim about the strength of the gravitational force exerted on the rock as the rock gets farther from the asteroid.
For the first throw, state a claim about the relationship about the strength of the gravitational force exerted on the rock as the rock gets farther from the asteroid and the behavior indicated between time 0 and t1 in the velocity-time graph.
For the second throw, state a claim about why there is a horizontal asymptote for the velocity.