Question 106434This question is from textbook Mechanics I
: Hey again! :D
A particle has position 2i + j initially and is moving with speed 10ms-1 in the direction 3i - 4j. Find it's position vector when t = 3 and the distance it has travelled in those 3 seconds.
I know the distance travelled is Speed * time, so 10 * 3 = 30metres.
I have already posted this topic, because the people gave the correct answers, ( thanks alot to you all for helping! :P )
but i still dont understand how you got them, i thought, if in 1 second, you do 3i - 4j
then in 3 seconds you do, 9i - 12j, add on the original, so 11i - 11j,
i have no idea how you got to 20i and 23j, i can see with 3i-4j, if you multiply everythign by 6, you get a figure that once added to the original 2i + j, gives the answer, but again why 6? :( Thanks again in advanced
This question is from textbook Mechanics I
Found 2 solutions by Fombitz, scott8148:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! You start at (2,1)
In one second you move 10 meters or directionally (6,-8) since
6,8,10 are the Pythagorean triple (3,4,5)x2.
So in one second you are at (using ordered pair(vector) addition),
(2,1)+(6,-8)=(8,-7)
After another second you move another (6,-8)
(8,-7)+(6,-8)=(14,-15)
and after the third second, you move another (6,-8)
(14,15)+(6,-8)=(20,-23)
If you went on another second, you would move to
(20,-23)+(6,-8)=(26,-31)
and so on.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! you'll notice that the displacement you think should happen (9i-12j) is half of the correct one (18i-24j)
the direction vector (3i-4j) has a resultant of magnitude 5 (3, 4, 5 triangle)
...when you apply these proportions to the known resultant of 30 you get 18, 24, 30
...the 6 is the ratio between 5 and 30
...your answer was half the correct value because you multiplied by 3 (the 3 sec), but not the 2 ((10m/sec)/5)
|
|
|
