Aprojectile is shot directly away from earth's surface. neglect the rotation of the earth.
what multiple of earth's radius re gives the radial distance (from the earth's center) the projectile reaches if
(a) its initial speed is 0.351 of the escape speed from earth and
(b) its initial kinetic energy is 0.351 of the kinetic energy required to escape earth? (give your answers as unitless numbers.)
(c) what is the least initial mechanical energy required at launch if the projectile is to escape earth?

Explanation:

We shall apply law of  conservation of mechanical energy for projectile being thrown .

Total energy on the surface = total energy at height h required

a ) At height h , velocity = .351 x ( 2 GM/R x h )

h = .14 R

b )

h = .54 R

c ) least initial mechanical energy required at launch if the projectile is to escape Earth

= GMm / R + 1/2 m (2GM/R)

= 0

there was no answer choices but i think its representative

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: