20 m A projectile is fired from the origin (at y = 0 m) as shown in the diagram. The initial velocity components are Vox = 310 m's and Vov = 26 m s The
projectile reaches maximum height at point P. then it falls and strikes the ground at point Q which is 20 m below the launch point. What is the horizontal
distance that the projectile travels (labeled x in the diagram)?
O 1.3 km
700 m
O 32 km
O 870 m
O 1.9 km

  1.9 km

Explanation:

The equation for vertical motion is ...

  h(t) = -4.9t^2 +26t +20

This will have a zero near t = 5.988 seconds.*

The horizontal distance traveled in that time is ...

  (310 m/s)(5.988 s) ≈ 1856 m ≈ 1.9 km

_____

* The root of a quadratic can be found numerous ways. We choose the quick and easy: let a graphing calculator show it to you.

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: