Suppose that a wind is blowing in the direction s45°e at a speed of 30 km/h. a pilot is steering a plane in the direction n60°e at an airspeed (speed in still air) of 100 km/h. the true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. the ground speed of the plane is the magnitude of the resultant. find the true course and the ground speed of the plane.

The true course: north of east

The ground speed of the plane: 96.68 m/s

Explanation:

Given:

= velocity of wind = = velocity of plane in still air =

Assume:

= resultant velocity of the plane = direction of the plane with the east

Since the resultant is the vector addition of all the vectors. So, the resultant velocity of the plane will be the vector sum of the wind velocity and the plane velocity in still air.

Let us find the direction of this resultant velocity with respect to east direction:

This means the the true course of the plane is in the direction of north of east.

The ground speed will be the magnitude of the resultant velocity of the plane.

Hence, the ground speed of the plane is 96.68 km/h.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Answer(b) both involve the use of levers;