I would like someone to double-check my answers on this question:
River currents (miles per hour) at a certain location are given below. The current direction at this location was “from the north” during the time interval shown, and the current did not exhibit any severe fluctuations other than those shown in the chart.
Chart:
time of day: 6:00 6:10 6:20 6:30 6:40
speed (mph): 17 20 22 21 17
A. Using trapezoids, estimate the average river current speed from the north from 6:00 AM until 6:40 AM. (i got 0.333miles)
B. At approximately what time between 6:00 AM and 6:40 AM would you estimate that the river current had the average velocity? ( i got approx. 6:10)
C. A message in a bottle near this location is released at 6:00 AM. Assuming that the bottle travels along with the river’s current, approximately how far south will the bottle be at 6:40 AM? ( i got the distance traveled would be the 13.33 mi)
D. What is the average acceleration of this bottle from 6:00 AM to 6:40 AM? ( i got 0.025 mi/min^2)
Thank you for any help!
a. how can the average be much less than the lowest river velocity?
b. Doesn't the data show at 6:10 the velocity was 20?
c. distance=avgvelocity*time
time= 2/3 hr So I don't know exactly what you used for avg velocity. See a) above.
d.avg acceleration=(vf-vi)/time
= (17-17)/time= zero
I did
(0.5)(10)(0.283+0.333) + (0.5)(10)(0.333+0.367) + (0.5)(10)(0.367+0.350) + (0.5)(10)(0.350+0.283)
= 13.33 miles
Avg value: (13.33) / 40 = 0.333 mi/min
so 19.98 miles per hour (converting the mi/min to mph) would be my actual average i suppose whoops
Which would give B. as being 6:10, or maybe about 6:09 since the velocity is riiiight under 20
for c.) d=v*t where v=19.98 and t=2/3, 19.98*(2/3)= 13.32 (which is actually one decimal off of my answer oops)
I think the problem was I hadn't converted my units. Does this make sense now?
To double-check your answers, let's go through each question and see if our calculations match.
A. To estimate the average river current speed, we can use the trapezoid rule. The formula for finding the area using the trapezoid rule is:
Average speed = (sum of speeds * time interval) / total time
Using the given data:
Sum of speeds = 17 + 20 + 22 + 21 + 17 = 97
Time interval = 6:40 AM - 6:00 AM = 0 hours and 40 minutes = 2/3 hours
Total time = 6:40 AM - 6:00 AM = 0 hours and 40 minutes = 2/3 hours
Average speed = (97 * 2/3) / (2/3) = 97 miles per hour
So, the average river current speed is 97 miles per hour, not 0.333 miles.
B. To estimate the time when the river current had the average velocity, we can take the midpoint of the time interval. The time interval is from 6:00 AM to 6:40 AM, which is 40 minutes. The midpoint is halfway between these times, which is 20 minutes after 6:00 AM.
So, the estimated time when the river current had the average velocity is approximately 6:20 AM, not 6:10 AM.
C. To determine how far the bottle would have traveled from 6:00 AM to 6:40 AM, we can calculate the average speed and multiply it by the time interval.
Average speed = (17 + 20 + 22 + 21 + 17) / 5 = 19.4 miles per hour
Time interval = 6:40 AM - 6:00 AM = 0 hours and 40 minutes = 40/60 = 2/3 hours
Distance traveled = Average speed * Time interval = 19.4 * (2/3) = 12.933 miles
So, the approximate distance the bottle would have traveled from 6:00 AM to 6:40 AM is 12.933 miles, not 13.33 miles.
D. To find the average acceleration of the bottle, we need to divide the change in velocity by the change in time.
Change in velocity = Final velocity - Initial velocity
= 17 - 17 = 0 miles per hour
Change in time = 6:40 AM - 6:00 AM = 40 minutes = 40/60 = 2/3 hours
Average acceleration = Change in velocity / Change in time = 0 / (2/3) = 0 miles per hour per hour, or 0 mi/min^2
Therefore, the average acceleration of the bottle from 6:00 AM to 6:40 AM is 0 mi/min^2, not 0.025 mi/min^2.
I hope this helps! Let me know if you have any further questions or need more clarification.