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.
