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

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In summary, Cathy is asking for help with a vector question involving two ice skaters, John and Norma, who are initially at positions (40,0) and (0,20) and moving with constant velocities of 5i and (3i+4j) respectively. She also asks for help with another question involving John's change in position vector and velocity. Cathy also asks for help with three more vector questions involving parallel vectors, vector magnitude, and an aircraft's position and velocity.
  • #1
CathyLou
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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
 
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  • #2
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.
 
  • #3
"Hint":
Zeroes are nothing, so they can just be removed, can't they? :smile:
 
  • #4
Thanks so much for your help.

I get it now.

Cathy
 
  • #5
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
 
  • #6
(a) How are parallell vectors related to each other?
(b) Similar.
(c) How are magnitude related to vector components?
 
  • #7
Thanks for your help.

I have worked out the answers now. :)

Cathy
 
  • #8
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
 
Last edited:

1. What is the M1 Vector Question: John & Norma's Ice Skating Adventure?

The M1 Vector Question is a scientific question or problem that involves using vector calculations to solve a real-world scenario. In this case, the scenario involves John and Norma's ice skating adventure, where they are trying to determine the velocity and direction of their movement on the ice.

2. Why is it important to use vector calculations in this scenario?

Vector calculations are important in this scenario because they take into account both magnitude (speed) and direction of movement. This is essential for accurately representing the movements of John and Norma on the ice, as well as predicting their future movements.

3. What information do we need to solve the M1 Vector Question?

To solve the M1 Vector Question, we need to know the initial position and velocity of John and Norma, as well as any external forces acting on them (such as friction from the ice). We also need to know the mass and direction of their movements.

4. How do vector calculations help us in understanding the physics of John and Norma's ice skating adventure?

Vector calculations allow us to break down the complex movements of John and Norma into simpler components, such as their x and y directions. This helps us understand the physics of their adventure by showing us how different forces and movements are affecting their overall motion.

5. What are some real-world applications of the M1 Vector Question?

The M1 Vector Question can be applied to a variety of real-world scenarios, such as analyzing the motion of objects in sports like ice skating, hockey, or skiing. It can also be used in engineering and navigation, such as calculating the trajectory of a rocket or determining the direction and speed of a ship's movement.

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