How do i solve this vector mechanics question?

A boat travels in a straight line at constant speed
initially the boat has position(-11i-2j)km relative to fixed origin O.
After 90 minutes the boat has position(i+6j) relative to O.
(a) show that the speed of the boat is p\/13 kmh-1, where p is a constant to be found

The boat continues in the same direction until it reaches a point X.
Given that X is due north east of O
(b) find the position vector X, making your method clear.

Reply 1

tonyiptony

11

Please do show any thoughts/workings you have so far. We don't do the problem for you here on TSR.

That said, starting by sketching how the boat moves is always a good idea.

Reply 2

davros

16

Original post by IO bear

A boat travels in a straight line at constant speed
initially the boat has position(-11i-2j)km relative to fixed origin O.
After 90 minutes the boat has position(i+6j) relative to O.
(a) show that the speed of the boat is p\/13 kmh-1, where p is a constant to be found

The boat continues in the same direction until it reaches a point X.
Given that X is due north east of O
(b) find the position vector X, making your method clear.

As above, plus do you understand what you're being asked in the question? What is the definition of speed? How does it relate to velocity? How do you work out velocity (a vector quantity)?

Upload some working and we can help further :smile:

Reply 3

IO bear

OP

10

Original post by davros

As above, plus do you understand what you're being asked in the question? What is the definition of speed? How does it relate to velocity? How do you work out velocity (a vector quantity)?

Upload some working and we can help further :smile:

i have done (a) to get the constant p is 8/3 -not sure if that's right
for (b) i think that X is k(i+6j) where k is a constant to be found
not sure where to go from there . I know that the speed is constant but not sure about the time
many thanks

Reply 4

davros

16

Original post by IO bear

i have done (a) to get the constant p is 8/3 -not sure if that's right
for (b) i think that X is k(i+6j) where k is a constant to be found
not sure where to go from there . I know that the speed is constant but not sure about the time
many thanks

I haven't checked your speed but hopefully you computed velocity (as a vector) = change in position / time then used the magnitude of that velocity vector for the speed.

For the second part, do you know what "north east of O" means in vector terms?

Reply 5

IO bear

OP

10

Original post by davros

I haven't checked your speed but hopefully you computed velocity (as a vector) = change in position / time then used the magnitude of that velocity vector for the speed.

For the second part, do you know what "north east of O" means in vector terms?

yes that's exactly how i calculated the velocity. i'm guessing north east means in a positive direction? like a compass?

Reply 6

davros

16

Original post by IO bear

yes that's exactly how i calculated the velocity. i'm guessing north east means in a positive direction? like a compass?

yes but you can be a bit more precise than that - e.g. north would be "only in the j-direction, no i-component", east would be "only in the +ve i direction etc". What does "north-east" look like in terms of what it tells you about the relative i- and j-components? Try drawing a right-angled triangle with the hypotenuse pointing north-east and think about what the angles are in that triangle and what it means for the sides.

Reply 7

IO bear

OP

10

Original post by davros

yes but you can be a bit more precise than that - e.g. north would be "only in the j-direction, no i-component", east would be "only in the +ve i direction etc". What does "north-east" look like in terms of what it tells you about the relative i- and j-components? Try drawing a right-angled triangle with the hypotenuse pointing north-east and think about what the angles are in that triangle and what it means for the sides.