Suppose a ship heads directly north away from the docks in a harbor at a speed of 3.80 km/h. after traveling 2.50 km, the ship leaves the harbor encountering an ocean current moving due west at 3.00 km/h. find the location of the ship (distance from the dock in km and direction in degrees counterclockwise from the east) 1.00 h after it leaves the dock if it does not change its direction relative to the ocean.

   R = 3,936 km      θ=105º

Explanation:

This is a problem of vector addition, let's find it takes time for the ship to reach the ocean

      v1 = x1 / t1

      t1 = 2.50 / 3.80

      t1 = 0.658 h

Let's analyze how much travel time is left

       t2 = 1 h - t1

       t2 = 1 - 0.658

       t2 = 0.342 h

This is the time he walked by the ocean, let's calculate every distance he traveled

X axis

          v2 = -3.00 km / h

          x = v t

          x2 = -3.00 * 0.342

          x2 = - 1,026 km

Axis y

         v1 = 3.80 km / h

         y2 = v1 t2

         y2 = 3.80 0.342

         y2 = 1.30 km

The total distance on each axis is

         xall = x2

         xall = -1,026 km

         y all = 2.5 + y2

        y  all = 2.5 + 1.3

        y all = 3.8 km

Let's calculate the distance and angle from the pier with the Pythagorean theorem and trigonometry

       R² = xall² + yall²

       R = √(1,026² + 3.8²)

       R = 3,936 km

       tan θ = yall / xall

       tan θ = 3.8 / 1.026

        θ = tan -1 (3.70)

      θ = 75º

The angle measured from the x axis (East) is 180 - 74 = 105º

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

explanation:

v=uf/(u-f)

= 5.-10/(5+10) convex lens has negative focal length