The following figure shows several of coach\'s positions at various times At eac

Question

The following figure shows several of coach's positions at various times At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D. What is the coach's resulting displacement and distance of travel? A plane flies northwest out of O'Hare Airport in Chicago at a speed of 400 km hr in a direction of 150 degrees (i.e., 30 degrees north of west). The Canadian border is located a distance of 1500 km due north of Chicago. The plane will cross into Canada after approximately 0.13 0.23 0.27 3.75 4.33 6.49 7.50 None of these are even close.

Explanation / Answer

Hi,

1. Here we have to remember the difference between displacement and distance.

- The displacement is a vector, so it has sense and direction

- The distance is a number and it is always bigger than 0.

The total displacement can be found doing the following:

d = xf - x0 ; where d is the displacement, xf is the final position and x0 is the initial position.

d = (-5 yd) - (50 yd) = -55 yd

The result obtained means that the coach has travelled 55 yd from its initial position to the negative direction (the sense depends on the coordinate system).

The distance travelled can be calculated as:

- Distance from A to B : d = 50 yd - 15 yd = 35 yd

- Distance from B to C : d = 35 yd - 15 yd = 20 yd

- Distance from C to D : d = 35 yd - (-5 yd) = 40 yd

- Total distance: d = 20 yd + 35 yd + 40 yd = 95 yd

2. In this case we have to find the vertical component of the speed of the plane, as said component will tell us when the plane has crossed the border.

u = v sin (150°) = (400 km/h) (1/2) = 200 km/h

Note: we use the vertical component because the distance to the border is given in that direction.

If we assume that the plane maintains the same speed throughout the travel, we have the following:

x = u*t :::::::: t = x/u = 1500 km / (200 km/h) = 7.5 h

So, the plane should be crossing the border after 7.5 h of taking off from the airport.

I hope it helps.

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