This is in my Vectors lesson

Question

A balloon is flying at a constant speed of 20 mi / h at a bearing of N 36° E. There is a 10 mi / h crosswind blowing due east. What are the balloon's actual speed and direction? Round angles to the nearest degree and other values to the nearest tenth.

Answer 1

Hi Brooke, using the balloon speed and given angle, the x-component is: cos Θ = x / 20 and the y-component is sin θ = y / 20

x = 20 * cos 36, or 16.2 mph

y = 20 * sin 36 = 11.8 mph

Adding the x-component, 16.2 mph, plus the wind speed, 10 mph, gives a new x-component of 26.2 mph.

The adjusted wind speed is: √(26.2² + 11.8²), or 28.7 mph.

The adjusted angle of travel is: tan^-1 θ = 11.8 / 28.7, or 24 degrees rounded.

Questions?