Starting from a location with position vector π1,π₯=β17.5 m and π1,π¦=23.1 m , a rabbit hops around for 10.7 seconds with average velocity π£ππ£,π₯=β2.25 m/s and π£ππ£,π¦=1.79 m/s . Find the components of the position vector of the rabbit's final location, π2,π₯ and π2,π¦ .
To find the components of the position vector of the rabbit's final location, we can use the formula:
π2,π₯ = π1,π₯ + π£ππ£,π₯ * π‘
π2,π¦ = π1,π¦ + π£ππ£,π¦ * π‘
Given:
π1,π₯ = -17.5 m
π1,π¦ = 23.1 m
π£ππ£,π₯ = -2.25 m/s
π£ππ£,π¦ = 1.79 m/s
π‘ = 10.7 s
Substituting the given values into the formulas, we get:
π2,π₯ = -17.5 m + (-2.25 m/s) * 10.7 s
π2,π¦ = 23.1 m + (1.79 m/s) * 10.7 s
Simplifying, we have:
π2,π₯ = -17.5 m - 24.075 m = -41.575 m
π2,π¦ = 23.1 m + 19.193 m = 42.293 m
Therefore, the components of the position vector of the rabbit's final location are:
π2,π₯ = -41.575 m
π2,π¦ = 42.293 m
To find the components of the position vector of the rabbit's final location, we can use the average velocity and the time period.
The average velocity is given as:
π£ππ£,π₯ = -2.25 m/s
π£ππ£,π¦ = 1.79 m/s
And the time period is given as:
π‘ = 10.7 seconds
To find the components of the position vector of the rabbit's final location, we can use the following equations:
π2,π₯ = π1,π₯ + π£ππ£,π₯ * π‘
π2,π¦ = π1,π¦ + π£ππ£,π¦ * π‘
Substituting the given values, we can calculate:
π2,π₯ = (-17.5 m) + (-2.25 m/s) * (10.7 s)
π2,π¦ = (23.1 m) + (1.79 m/s) * (10.7 s)
π2,π₯ = -17.5 m - 24.075 m
π2,π¦ = 23.1 m + 19.193 m
π2,π₯ = -41.575 m
π2,π¦ = 42.293 m
Therefore, the components of the position vector of the rabbit's final location are π2,π₯ = -41.575 m and π2,π¦ = 42.293 m.