Question

A plane flies a square route, with each side 1500m in length (north, west, south, then east). If there is a wind blowing from the east at 20km/h during the whole trip, find the total time it will take the plant to completethe journey. The airspeed of the plane is 80km/h.

Answer 1

When the plane is flying north and south, the wind is perpendicular to the plane. Therefore, the wind has no effect on the plane's speed relative to the ground. Its speed relative to the ground is 80km/hr.

When the plane is flying east, the plane is seeing a head wind. Therefore, the plane's speed relative to ground will be 80-20.

When the plane is flying west, the plane is seeing a tail wind. Therefore, the plane's speed relative to the ground will be 80+20.

Noting that\[\rm displacement = velocity \times time\]We can set up an expression for the time it takes to travel a distance d while travelling at a velocity v as\[t = {d \over v}\]If we sum up the time it takes to travel north, south, east, and west; we will get the following\[t = {d \over v_n} + {d \over v_s} + {d \over v_e} + {d \over v_w}\]\[t = {1.5 \over 80} + {1.5 \over 80} + {1.5 \over 80 -20} +{1.5 \over 80+20}\]Time will be in hours. Multiply by 60 to find the time in minutes or 3600 to find the time in seconds.

Answer 2

@eashmore, that makes sense to me, but the correct answer is listed as 284 seconds. I'm getting 279. Any ideas?

Answer 3

I'm also getting 279. No ideas. Sorry.