Question Video: Identifying Displacement–Time Graphs for a Projectile | Nagwa Question Video: Identifying Displacement–Time Graphs for a Projectile | Nagwa

# Question Video: Identifying Displacement–Time Graphs for a Projectile Physics • First Year of Secondary School

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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 displacement of 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 displacement of the object between leaving the ground and returning to the ground? (A), (B), (C), or (D).

In this question, we have an object launched with a diagonally upward force. And we want to identify the graph that correctly shows the change in horizontal displacement over time. Initially, the object has zero horizontal displacement. The diagonally upward force has a horizontal component responsible for the horizontal velocity of the object. After the object is launched, its horizontal velocity will remain constant.

Now let’s recall that the slope of a displacement–time graph is equal to the velocity. We can write this as 𝑣 equals Δ𝑠 over Δ𝑡, where 𝑣 is the velocity, 𝑠 is the displacement, and 𝑡 is the time. Since we know that the horizontal velocity of the object remains constant, this means that the slope of the displacement–time graph must also remain constant.

Now, let’s consider each graph in order. Graph (A) shows a changing slope, so this means that the horizontal velocity will change. Therefore, the horizontal velocity is not constant in this graph, so graph (A) is incorrect.

Graph (B) has a constant slope, so this looks like a good representation of how the horizontal displacement of the object changes.

Graph (C) shows a changing slope, so this means that the horizontal velocity will change. Therefore, the horizontal velocity is not constant in this graph, so graph (C) is incorrect.

Graph (D) has a constant slope. However, this graph shows the object having an initial nonzero horizontal displacement. It also shows a constant value for the horizontal displacement, which suggests that the object did not move horizontally. So graph (D) is incorrect.

Therefore, graph (B) must be the correct answer. Graph (B) correctly shows the changes in the horizontal displacement of the object between leaving the ground and returning to the ground.

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