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Question Video: Identifying Distance–Time Graphs for a Projectile Physics • 9th Grade

An object is set in motion by an initial force 𝐹 that acts diagonally upward, as shown in the diagram. The object undergoes projectile motion. Which of the following graphs shows the changes in the horizontal distance moved by the object between leaving the ground and returning to the ground? [A] Graph A [B] Graph B [C] Graph C [D] Graph D

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Video Transcript

An object is set in motion by an initial force 𝐹 that acts diagonally upward, as shown in the diagram. The object undergoes projectile motion. Which of the following graphs shows the changes in the horizontal distance moved by the object between leaving the ground and returning to the ground? (A), (B), (C), or (D).

In this question, we want to determine the graph that correctly shows the changes in the horizontal distance of the object during the projectile motion. First, we will look at the diagram. The force acts diagonally upwards. So this indicates that the object has an initial horizontal velocity and an initial vertical velocity, which are both nonzero. The question does not indicate the presence of any force that acts horizontally on the object other than the force responsible for the initial horizontal velocity of the object.

In addition, the acceleration of the object throughout its motion is entirely vertical. So this means that the horizontal component of the velocity will remain constant throughout the projectile motion. We can recall the equation speed equals distance over time. So we know that distance is equal to speed multiplied by time. Since the horizontal velocity is constant, this means that the horizontal speed is constant. Since the horizontal speed remains constant, then the equation tells us that the horizontal distance is directly proportional to time.

Now that we know how the horizontal distance changes with time, we can look at the graphs in the answer options.

Looking at graph A, we see that the horizontal distance remains constant with time and always remains at the same distance from the origin. This is not possible because this suggests that the object did not move horizontally, meaning that the horizontal speed is zero. We know that this is not true because the object has a horizontal velocity provided by the initial force 𝐹. So graph (A) is incorrect.

In graph (B), we see that the object starts at some horizontal distance away from the origin and then decreases linearly with time. This is not correct because this suggests that the object is approaching the point of launch. So graph (B) is incorrect.

In graph (C), we see that the initial distance starts at zero, and the horizontal distance does increase linearly with time. So graph (C) looks like the correct answer.

Just to be sure, let’s look at graph (D). In this graph, we see that the object moves away a certain distance and then returns to the beginning. This is incorrect because the object does not return to its point of origin. So graph (D) must also be incorrect.

Therefore, we are left with graph (C), which must be the correct answer. Graph (C) correctly shows the changes in the horizontal distance moved by the object between leaving the ground and returning to the ground.

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