I would be very appreciative if someone could provide me with the formula I would use to plug these figures into a graph.
3. A 2m length of board rests with one end on the floor and the other end on a small stack of bricks. A baseball is rolled up the board and back down again in a total of 4 seconds. The farthest the baseball reached on the board was 130cm.
This is the same problem as a ball rolls down a board making an angle θ with the horizontal in t=2 seconds over a distance S of 1.3 m.
We ignore the size of the ball, which can slow down the ball.
Let g=acceleration due to gravity = 9.8 m/s²
then
a=acceleration down the board
=g sin(θ)
vi=initial velocity=0
and total time to travel S=1.3 m t,
then
S=vi*t + (1/2)g sin(θ)t²
Solve for θ.
To graph the motion of the baseball rolling up and down the board, you can use the equation of motion for an object under constant acceleration:
distance = initial velocity * time + 0.5 * acceleration * time^2.
In this scenario, the baseball starts from rest, so the initial velocity is 0. We know the time it takes for the baseball to complete the round trip is 4 seconds. However, we do not have information about the acceleration.
Given that the board is inclined, gravity will act as an acceleration force. The acceleration will depend on the angle of the board. To calculate the acceleration due to gravity on the inclined board, we need to consider the vertical and horizontal components of the gravitational force.
The vertical component of the gravitational force is given by:
mg * cos(theta), where m is the mass of the baseball and theta is the angle of the incline.
The horizontal component of the gravitational force is given by:
mg * sin(theta).
Since the board is at an angle, the vertical acceleration due to gravity will not affect the motion of the baseball along the board. Therefore, we only need to consider the horizontal acceleration due to gravity.
With the horizontal component of the gravitational force, we can calculate the acceleration using the equation:
force = mass * acceleration.
So, mg * sin(theta) = mass * acceleration.
Once we have the acceleration value, we can use the equation of motion to calculate the distance traveled by the baseball on the board in each second.
To plot the graph, you would create a time-distance graph with time on the x-axis and distance on the y-axis. Time would vary from 0 to 4 seconds, and the distance traveled by the baseball on the board would be calculated using the equation of motion at each second. The data points calculated can then be plotted on the graph to show the motion of the baseball.