Aqa AS Maths M1(mechanics) help

At time 0900, a snowmobile passes a fixed origin O with constant velocity (8i-14j) kmh-1, where i and j are unit vectors due east and due north respectively. An hour and a half later, the snowmobile changes velocity so that it is travelling due west with speed 20kmh-1.

a) at what time is the snowmobile due south of O?

help with these times of questions and general mechanics tips for these topics would be good sorry for asking so much but I dont want mechanics to bring me down especially if they have questions like these that are phrased differently

At time 0900, a snowmobile passes a fixed origin O with constant velocity (8i-14j) kmh-1, where i and j are unit vectors due east and due north respectively. An hour and a half later, the snowmobile changes velocity so that it is travelling due west with speed 20kmh-1.

a) at what time is the snowmobile due south of O?

help with these times of questions and general mechanics tips for these topics would be good sorry for asking so much but I dont want mechanics to bring me down especially if they have questions like these that are phrased differently

What specific bit confuses you?

At time 09:00, let's call this our original position. Using displacement = speed * time we have our position vector at any time t as

(0, 0) + t (8, -14).

We want our position 1 and a half hours later. That's (0, 0) + 1.5 (8, -14).

Simplify that.

Travelling due west with speed 20 kmh^-1 is the same as saying it has a constant velocity of (-20, 0). But it's starting at 1.5(8, -14).

So its position at a general time t is 1.5(8, 14) + t(-20, 0).

What does it mean for the thing to be due south of O, it means that it's 'i' component is 0, right? Draw a graph and label a point right underneath the origin, what is the i component of that?

So you have the i component as 1.5(8) - 20t which can set to 0 and solve.

What specific bit confuses you?

At time 09:00, let's call this our original position. Using displacement = speed * time we have our position vector at any time t as

(0, 0) + t (8, -14).

We want our position 1 and a half hours later. That's (0, 0) + 1.5 (8, -14).

Simplify that.

Travelling due west with speed 20 kmh^-1 is the same as saying it has a constant velocity of (-20, 0). But it's starting at 1.5(8, -14).

So its position at a general time t is 1.5(8, 14) + t(-20, 0).

What does it mean for the thing to be due south of O, it means that it's 'i' component is 0, right? Draw a graph and label a point right underneath the origin, what is the i component of that?

So you have the i component as 1.5(8) - 20t which can set to 0 and solve.

oh wow thanks alot that really clears things up and generally i get lost in these type of questions either that or i try something and its not the right answer this helps alot i might have more questions hope i dont get annoying thanks alot

Is that right? Got a little confused.

Yeah, that's correct. It wants the time though, so what's 9 o'clock + 2.1 hours?

Hint: it's 11 o'clock + (0.1 * 60) minutes.

so 9 + 2 hours and six mins? so 1106

Sounds right, yeah.

ok i think im getting the topic more because ive been doing the questions(slowly but still) and getting the right answers

Awesome.

thans again i might have mre questions though cus im going through the other topics etc