00:01
We'd like to determine the velocity of our airplane.
00:03
So the velocity of our plane with respect to the air, so vp .c comma a, is equal to our speed, which is 300 miles per hour, times cosine of 30 degrees, plus 300 times sign of 30 degrees.
00:22
So vp minus va is equal to, we have, now we just plug this into a calculator.
00:39
We have our 300 times cosine of 30 degrees, which is 259 .8, and that's going to be ihat plus 150 j -hat.
01:01
J -hat will be in here, and this is miles per hour.
01:05
Now the velocity of the plane with respect to the ship is equal to our 280 times cosine of 33 degrees i -hat plus 280 sign of 33 degrees j -hat so vp minus vs is equal to now we just plug that into a calculator 280 times cosine of 33 degrees is 23 .8 i -hat plus now our 280 sign of 33 degrees 152 .4 j hat and miles per hour so now a velocity of velocity.
01:48
Of our plane also the velocity of the ship is given in our problem our velocity of our ship is negative 12 miles per hour due south so that is j hat so now our velocity of our plane is equal to our value of 234 .8 plus plus our value of plus 152 .4 minus 12 j hat.
02:44
J hat and that's i hat.
02:46
So now our velocity of our plane, we take our square root, or let's first find what this is.
02:52
This is 234 .8 i hat plus our 152 .4 minus 12, which is 140 .4.
03:02
So the velocity of our plane is our vpx squared plus vp y squared.
03:08
So we take our squared of that.
03:10
So we take our square root of 234 .8 squared plus 140 .4 squared, which is 273 .5 miles per hour...