A marker is rolled horizontally off the top of a table. after 5 econds the marker lands on the ground with a final velocity of -2.5 m/s which kinematic equation would be most useful for finding the balls initial velocity
The kinematic equation that would be most useful for finding the marker's initial velocity is the equation that relates the final velocity, initial velocity, time, and acceleration:
v = u + at
where:
v = final velocity (-2.5 m/s),
u = initial velocity (unknown),
a = acceleration (can be assumed as the acceleration due to gravity, which is approximately -9.8 m/s^2), and
t = time (5 seconds).
By rearranging the equation, we can solve for the initial velocity:
u = v - at
Plugging in the known values:
u = -2.5 m/s - (-9.8 m/s^2)(5 s)
u = -2.5 m/s + 49 m/s
u = 46.5 m/s
To find the initial velocity of the marker, we can use the kinematic equation that relates the final velocity (vf), initial velocity (vi), time (t), and acceleration (a):
vf = vi + at
In this case, the marker is rolling horizontally, so we can assume that the acceleration is due to gravity acting vertically downward. The acceleration due to gravity is typically represented as -9.8 m/s^2 since it acts in the opposite direction of positive velocities.
Since the marker lands on the ground, we can assume that its displacement in the vertical direction (y-direction) is equal to the height of the table. Let's denote the height of the table as h.
The marker is at rest initially (vi = 0 m/s) and has a final velocity of -2.5 m/s. The acceleration due to gravity remains constant (-9.8 m/s^2). The time it takes for the marker to fall is 5 seconds.
Substituting these known values into the kinematic equation:
-2.5 m/s = 0 m/s + (-9.8 m/s^2)(5 s)
Now, we can solve for the initial velocity, vi:
vi = -2.5 m/s + (9.8 m/s^2)(5 s)
Simplifying the equation, we get:
vi = -2.5 m/s + (-49 m/s)
Finally, calculating the sum:
vi = -51.5 m/s
So, the initial velocity of the marker is approximately -51.5 m/s.
To find the ball's initial velocity, we can use the following kinematic equation:
v = u + at
Where:
- v is the final velocity (-2.5 m/s in this case)
- u is the initial velocity (what we want to find)
- a is the acceleration (-9.8 m/s^2 due to gravity)
- t is the time (5 seconds in this case)
Rearranging the equation to solve for u, we have:
u = v - at
Substituting the known values into the equation:
u = -2.5 m/s - (-9.8 m/s^2 × 5 s)
Simplifying:
u = -2.5 m/s + 49 m/s
u = 46.5 m/s
Therefore, the ball's initial velocity is 46.5 m/s.