M1 Vector Question: John & Norma's Ice Skating Adventure

[CathyLou]

Hi.

Could someone please help me with the following M1 vector question? I would really appreciate it as I am really stuck.

At time t = 0, two ice skaters John (J) and Norma (N) have position vectors 40j metres and 20i metres relative to an origin O at the centre of an ice rink, where i and j are unit vectors perpendicular to each other. John has constant velocity 5i m/s and Norma has constant velocity (3i + 4j) m/s.

(a) Show that the skaters will collide an find the time at which the collison takes place.

I got that t is equal to 10 seconds and this is the correct answer in the back of the textbook.

(b) On another occasion, John has position vector 40j metres. He wishes to skate in a straight line to the point with position vector 30i metres. Given that is speed is constant at 5 m/s, find his velocity.

I drew a diagram and wrote down that 30i = 40j + vt, but I do not know where to go from here.

Thank you.

Cathy

 

[Doc Al]

You are given the magnitude of his velocity (5 m/s), you just need the direction. His change in position vector will be 30i - 40j; find a unit vector in that direction.

 

[arildno]

"Hint":
Zeroes are nothing, so they can just be removed, can't they?

 

[CathyLou]

Thanks so much for your help.

I get it now.

Cathy

 

[CathyLou]

Hi.

Could someone please tell me how to do the following vector question as I am really stuck.

8.

(a) Given that the vector ai + 3j is parallel to the vector 2i + 12j find a.

(b) Given that the vector 3i + bj is parallel to 12i - 20j find b.

(c) Given that the vector 7i + cj has magnitude 25 find the two possible values of c.

Any help would be really appreciated.

Thank you.

Cathy

 

[arildno]

(a) How are parallell vectors related to each other?
(b) Similar.
(c) How are magnitude related to vector components?

 

[CathyLou]

Thanks for your help.

I have worked out the answers now. :)

Cathy

 

[CathyLou]

This is the last question that I need to do but I am not sure how to start it. Could someone please help?

At 11:00 hours the position vector of an aircraft relative to an airport O is (200i + 30j) km, i and j being unit vectors due east and due north respectively. The velocity of the aircraft is (180i - 120j) km/h. Find:

(a) the time when the aircraft is due east of the airport O.

Thank you.

Cathy