A mosquito can fly with a speed of 1.10 m/s with respect to the air. Suppose a mosquito flies east at this speed across a swamp. The mosquito is flying into a breeze that has a velocity of 1.4 m/s with respect to Earth and moves in the direction of 35 west of south. What is the mosquito's speed with respect to the Earth?

The velocity of Mosquito with respect to earth will be 0.302m/s

Explanation:

V(ma) = 1.10 m/s, east  Velocity of mosquito with respect to air

V(ae) = 1.4 m/s at 35°  Velocity of air with respect to Earth in west of south direction.

Velocity of Mosquito with respect to earth will be  

V(me) = V(ma) + V(ae)

We need to find the mosquito’s speed with respect to Earth in the x direction.

V(x, me) = V(x, ma) + V(x, ae) = V(ma) + V(ae)(cos theta(ae) )

Angle (ae) = –90.0° − 35°=−125°

V(x, me) = 1.10 + (1.4)Cos(-125)

             = 1.10 + 1.4(-0.57)

             = 1.10 -0.798

              = 0.302

So the velocity of Mosquito with respect to earth will be 0.302m/s