Question
In an experiment, a student launches a ball with an initial horizontal velocity at an elevation 2 meters above ground. The ball follows a parabolic trajectory until it hits the ground. Which of the following accurately describes the graph of the ball's vertical acceleration versus time (taking the downward direction to be negative)?
- A negative value that does not change with time
- A gradually increasing negative value (straight line)
- An increasing rate of negative values over time
- (parabolic curve)
- Zero at all times since the initial motion is horizontal
Final Answer
(a)
Solution video
OpenStax College Physics for AP® Courses, Chapter 3, Problem 2 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. When a ball is launched horizontally and then it's in freefall basically, the only acceleration is horizontal. Here's a table, a leg, and this is two meters off the ground. The table top is two meters above the ground and the ball is launched horizontally. After it's no longer on the table top, there will be only one force on the ball assuming that we neglect air friction, and that force will be gravity, which is towards the center of the earth. It'll be straight down in other words, so when the ball is in freefall sometime later, its horizontal velocity, the horizontal component of its velocity will be unchanged. It will have some vertical component of velocity now, but what's important for this question is to answer the acceleration versus time. The acceleration will be due to this force. This is the force of gravity, and it is straight down and it's not going to change. I suppose that the ball does get closer to the center of the Earth and the force of gravity is related to that distance, its gravitational constant times the mass of the ball times the mass of the Earth divided by a distance to the earth center squared. But we can neglect that because this is a small change in distance. The answer here is that it's a negative value because we take up to be the positive direction in which case down and negative, and it has not changed with time at all because the force on the ball is not changing with time.