In the Cartesian plane, a house is at the point (107, 64). We are currently at t
ID: 3113314 • Letter: I
Question
In the Cartesian plane, a house is at the point (107, 64). We are currently at the origin, and we want to reach this house. We have two modes of transportation:
•A magic carpet, which moves with a velocity vector of 3,1miles per hour (This means that, for every hour we’re on the carpet, we move 3 miles in the x direction and 1 unit in the y direction).
•A skateboard, which always moves with a velocity vector of 5,1 miles per hour (So, for every hour on the skateboard, we move 5 miles in the x direction and 1 mile in the y direction) Both of these vehicles have a “reverse” button, so they can also move with a velocity vector of 3,1and 5,1, respectively, if you want. Explain how long we should ride each of these vehicles to arrive at the house. Is there a location in the plane that we can’t reach using the magic carpet and the skateboard? Explain!!!
Explanation / Answer
We can't reach the point (107,64)
using magic carpet or skateboard.
Using magic carpet which has velocity (3,1) mile/hr
We need 64 hr to reach y co-ordinate of point (107,64)
But we end up reaching 192 mile in x direction .
So we reach point (192,64) instead of (107,64)
Similarly using skateboard with velocity (5,1) mile/hr
We end up reaching (320,64) after 64hrs.
So we can't reach the point from origin using magic carpet or skateboard.