What is the height of a projectile in 4 seconds if its initial height is 125 ft and it has a velocity of 300 ft per second? 972
1 answer:
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Part A
Answers: The braking distance is 25 meters for the dry road, 80 meters for the wet road, 140 meters for the icy road
As expected, the worse the conditions, the longer the skid.
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Explanation:
First locate the speed 50 km/hr. So you'll look at the horizontal axis which is the speed or velocity axis. The value 50 is at the midpoint between 40 and 60. Draw a vertical line straight up and down as far as you can go in both directions. Then mark the points of intersection between the vertical line and the various curves. Finally, draw horizontal lines from each of the points so you can see what the y coordinates are.
Check out figure 1 (attached image) to see a visual of what I'm referring to.
The points of intersection are roughly: (50,25) and (50,80) and (50,140). The first y values is an approximate guess because the visual graph given isn't perfectly lined up. The value is somewhere between 20 and 30 so 25 seems like a good compromise.
Therefore the braking distances are roughly 25, 80 and 140 for the dry, wet and icy roads (in that order).
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Part B
Answers: The top speeds required are 30 km/hr for the icy road, 45 km/hr for the wet road, 70 km/hr for the dry road
These are max speeds allowed so that the braking distance is 60 meters or less. This is the inverse order of part A. The worse conditions require a slower speed.
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Explanation:
We go in reverse of part A. Instead of looking on the x axis, we start with the y axis. Locate 60 on the y axis (which is the braking distance axis) which is between 40 and 80. In figure 2 (also attached), I draw a red horizontal line to start things off. Then I mark the points between each curve and the horizontal line. The last step is to drop vertical lines to the x axis to figure out the x coordinate of each red point.
The x coordinates are: 30, 45, 70
The 45 comes from the fact that it seems to be at the midpoint of 40 and 50 (this is a guess really).
So this means that a vehicle on an icy road can go at most 30 km/hr. A car on a wet road can't go faster than 45 km/hr. Finally a car on a dry road can have a top of speed of 70 km/hr. All of these road conditions will have a braking distance of 60 meters or less.
Answers:
Three points that solve the equation:
The graph is shown in the attached pictures.
NOTE: The first picture is the graph of the equation along with the plotted points, and the second one shows the work for those three points.
Step-by-step explanation:
1. To graph this equation, an easier way to do it would be to convert to slope-intercept form so we can graph knowing the y-intercept and the slope. Do this by isolating the y on the left side like so:
Remember that slope-intercept form is in y = mx + b format, and that m is the slope and b is the y-intercept. With this information, we know that (0, ) is the y-intercept and
is the slope of this equation. We can plot the point (0,
) on the graph, and then use the slope of
from there to graph other points and form a line. (When I graphed the line, I didn't include these "other points" so it wasn't confusing to locate which points were the three solutions listed.)
2. Points that solve an equation - or solutions - are also points that the line of the equation intersects. So, what we can do is form a table, plug in some x values into the equation, and solve for a y-value. The x and y values will form a point that is on the graph, thus they are solutions. (Please look at the second picture for work and clarification.) After identifying these points, just plot them on the graph and label them (as shown in the first picture).
