# Vector problem

Vector problem plz help!!!!

can any plz answer these 5 questions below
i have a physics test coming up and i dont get those questions
email me at [email protected] or [email protected] THX!!

1. a plane has a speed of 300 km/h relative to the surround air. The wind is blowing from a direction of 25 degree west of south at 40 km/h. Calulate the speed of the plane with respect to the ground. Also find the direction in which the plane would move if the polot flew the plane in such a manner that it was always pointed towards the north according to the planes compass

V=
Angle=

2. if the pilot of the plane in the above problem wish to fly directly towards the north, at what angle ( to the west of north) would the plane have to be pointed? Calculate the speed of the plane across the land in this case?

angle=
v=

3. assume that the pilot's intention had been to fly to a community 600 km directly norht of the starting point. How long wold the pilot expect the trip to last? use the plane's speed with respect to the air.

t=

4. considering the plane's actual path, how far from its intended destination is the plane after the time in quesiton #3? Begin by finding the displacement along the vector v using your value for the velocity with respect to the ground, from question #1

d=

5. using the velocity with respect to the ground from question #2 calculate how long it actually takes the plane to fly directly to the community that is 600 km to the north.

t=

thats all plz email me at [email protected] or [email protected]

$$\begin{multline*} \begin{split} &\vec{v_{pa}}=relative\ velocity\ of\ plane\ to\ air\\ &\vec{v_a}=relative\ velocity\ of\ air\ to\ ground\\ &\vec{v_p}=relative\ velocity\ of\ plane\ to\ ground\\ &\vec{v_{pa}}=300(cos\ \theta\vec{i}+sin\ \theta\vec{j})\\ &\vec{v_a}=40(cos\ 65^0\vec{i}+sin\ 65^0\vec{j})\\ &\vec{v_p}=V\vec{j}\ with\ V>0\\ &\vec{v_{pa}}=\vec{v_p}-\vec{v_a}\\ \end{split} \end{multline*}$$