An observer measured the angle of elevation of a mountain from a point on a level ground as 8.23 degrees. Moving 450 meters closer to the mountain, the angle of elevation is 9.44 degrees. All points are on the same vertical plane. What is the height of the mountain?

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A rocket is launched at ? = 0 seconds. Its height, in meters above sea-level, is given by the equationℎ = −4.9?2 + 325? + 227A. Find the time it takes the rocket to reach the maximum height? (Round answer to 2 decimal places.) B. What is the maximum height attained by the rocket? (Round to the nearest whole number)

Vector A⃗  has a magnitude of 9.30 m and is pointing in a direction of 25.0 degrees counterclockwise from the positive x axis. Vector B⃗  has a magnitude of 9.70 m and is pointing in a direction of 140. degrees counterclockwise from the positive x axis. What is A⃗ +B⃗ ? Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):

Langleyville (43 degrees S, 77.6 degrees w) and Cajun Country (25 degrees s, 77.5 degrees w) have almost the same longitude, which means that they are roughly due north-south of each other.  Set up all the work to find the approximate distance in miles between the cities assuming the radius of the earth is 4000 miles.

A plane is flying at a speed of 320 miles per hour on a bearing of N65°E. Its ground speed is 390 miles per hour and its true course, given by the direction angle of the ground speed vector, is 30°. Find the speed, in miles per hour, and the direction angle, in degrees, of the wind. The speed of the wind is miles per hour. (Do not round until the final answer. Then round to the nearest tenth as needed.)

On the map, let the +x-axis point east and the +y-axis north. An airplane flies at 880 km/h northwestward direction (i.e., midway between north and west). Can you help me visualize the components of the first velocity, and when the plane flies due south at the same velocity.  I understand the answer will be -622.25 for the run, meaning 880*cos(45) for x -axis; the y axis north is 880*sin(45) resulting in 622.5 Please help me visualize the first and second velocity when the plane flies due south at the same velocity?  Help me to visualize where one of the velocities due south is zero, and the other is whatever it is.   I am afraid I can properly visualize or understand in simple terms what is asked.  My point can you help to understand the right angle theorem to the angle.

Vector D = A+ B - C, where Ax=22, Ay= -12, Bx =5, By=-9, and C has a magnitude of 35 and points at +45 degrees. Use the analytical component method to calculate for Dx, Dy, and the angle of D.

An airplane is flying in the direction of 30° west of north. Windis blowing at 40 miles per hour from the south.a) What is the projection of the wind vector in the direction the airplaneis headed?b) What is the projection of the wind vector in the directionperpendicular to the direction the airplane is headed?

Hiker Harry walks 4 km east then 7 km 25o north of west. What is the magnitude and direction of Harry’s position after his hike as measured from his starting point? Give the angle measured relative to east. For example 90° means directly north.