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Scott, MIT Graduate

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An airplane flies due west at 150km/h with respect to the ...

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An airplane flies due west at 150km/h with respect to the air. There is a wind blowing at 95 km/h to the northeast relative to the ground. What is the plane's speed with respect to the ground?

You can think of this as a Pythagorean Theorem problem. The hypotenuse is the unknown. One short leg is the 150km/h minus the east component of the wind. The other short leg is the north component of the wind:

east comp: 95*cos(45) -- so the total leg is 150-95*cos(45)

north comp: 95*sin(45)

The magnitude of the velocity will be:

sqrt((150-95*cos(45))^2 + (95*sin(45))^2)

= 106.64 km/h

Let me know if you have any questions,

Scott

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Reply to Scott's Post: Can you also answer this one and i will add another $10.
You walk 20m south and 20m eas. Find the magnitude and direction of the resultant displacement both graphically and algebraically. Answer is 28.28 M what is the degrees counterclockwise from east?

Reply to Scott's Post: last one and i already accepted the last two and added in a bonus..
A weather station releases a balloon that rises at a constant 16m/s relative to the air, but there is a wind blowing at 6.0 m/s toward the west. What is the magnitude and direction of the velocity of the balloon? answer 17.07 m/s bu how many degrees above the horizontal?

That is what i had as well but it came up incorrect. Any other suggestions for that one.. the rest were all right.. does it change with the "above the horizontal"?

that didn't work either so maybe there is an error in the program.. let me know if you can think of anything else otherwise i will still accept this one because i had the same answer as well and appreciate your help..