A first object is thrown vertically upward with some initial speed and some initial height above the ground. Simultaneously, a second object is thrown straight down with the same initial speed and same initial height above the ground. Before the second object reaches the ground, the distance between the two objects _______as time advances. Ignore air resistance.
a)stays the same
b)increases than decrease
c)cannot by determined (not enough info.)
d)increases at an increasing rate
e)increases at a constant rate
The height y1 of the first object from the initial position, y0 with respect to time is given by the equation:
y1=ut-(1/2)gt²
Similarly, the height y2 of the second object is given by:
y2=-ut - (1/2)gt²
where
g=acceleration due to gravity, and
u=initial speed
The distance between the two objects is therefore given by y1-y2
=2ut
which is a linear function of time.
Make your choice of the answer and post it for checking if you wish.
To determine how the distance between the two objects changes as time advances, we need to consider the motion of each object separately.
Let's analyze the motion of the first object. It is thrown vertically upward with some initial speed and initial height above the ground. As it moves upward, it will eventually reach its maximum height and then start falling back down due to gravity. The motion of the first object is influenced only by the force of gravity acting against its initial upward velocity.
Now let's consider the motion of the second object. It is thrown straight down with the same initial speed and initial height above the ground as the first object. Since it is thrown downward, it is already moving in the direction of gravity. In this case, gravity adds to its initial downward velocity.
Based on this analysis, we can conclude that the second object will reach the ground before the first object does because it starts with an initial downward velocity.
Therefore, as time advances, the first object will still be moving upward while the second object is already falling downward. This means that the distance between the two objects will increase over time.
Hence, the correct answer is:
b) increases than decreases