Video Transcript
The object shown in the diagram is
undergoing two examples of projectile motion due to the forces 𝐅 one and 𝐅 two and
due to the object’s weight. The first example of a projectile
motion, example A, involves a launch angle for the object that is close to being
vertically upward. The other example, example B, shows
a launch angle that is much shallower, closer to being horizontal. For both examples, the horizontal
distance traveled by the object is the same. Which one of these statements about
the two objects is true? (A) Example A both has the greater
vertical velocity and is airborne for a longer time period. (B) Example A has the greater
vertical velocity but is not airborne for a longer time period. (C) Example B both has the greatest
vertical velocity and is airborne for a longer time period. (D) Example B has the greater
vertical velocity but is not airborne for a longer time period.
In this question, we want to
determine which example of projectile motion involves the greatest vertical velocity
and which involves the object being airborne for a longer time period. We will begin by considering the
vertical velocity.
On the diagram, we will mark the
height that example A reaches as ℎ sub A and the height that example B reaches as ℎ
sub B. We can also recall that in both
examples, the objects have the same constant downward acceleration due to gravity,
𝑔, acting on them. So let’s draw this on the
diagram. We can now see in the diagram that
example A is the one that travels a greater distance upwards. We also know that both examples
experience the same downward acceleration due to gravity. So, to reach a higher point,
projectile A must have a higher vertical velocity than projectile B. Therefore, we can eliminate answer
options (C) and (D).
Now, let’s consider the time period
that the object remains airborne. The time for which an object is in
the air is the time it takes for the vertical upward movement of the object to cease
and then for the object to fall back to the ground. When the objects are at their
highest points, both objects have zero vertical speed. We also know that the object in
example A has a greater vertical distance to travel to reach the ground than the
object in example B. Since both objects experience the
same downward acceleration due to gravity, 𝑔, we see that the object in example A
must take longer to fall back to the ground from its highest point than the object
in example B. This shows that the object in
example A is airborne for a longer time period than example B. Therefore, we can eliminate answer
option (B).
And this leaves us with answer
option (A), which is the correct answer. Example A both has the greater
vertical velocity and is airborne for a longer time period.
