Aprojectile of mass m is fired horizontally with an initial speed of v0 from a height of h above a flat, desert surface. neglecting air friction, at the instant before the projectile hits the ground, find the following in terms of m, v0, h and g: (a) the work done by the force of gravity on the projectile,
(b) the change in kinetic energy of the projectile since it was fired, and
(c) the final kinetic energy of the projectile. (d) are any of the answers changed if the initial angle is changed?

Answers:

a)

b)

c)

d) No

Explanation:

We have the following data:

is the mass of the projectile

is the initial speed of the projectile

is the height at which the projectile was fired

is the angle (it was fired horizontally)

is the acceleration due gravity

a) The Work when the applied force and the distance (height ) are parallel is:

(1)

Where is the force exerted by gravity on the projetile (its weight)

So:

(2)

(3) This is the work done by gravity

b) According to Conservation of energy principle the initial total mechanical energy is equal to the final mechanical energy  :

(4)

Where:

(5)

Being the initial kinetic energy and the initial gravitational potential energy

(6)

Being the final kinetic energy and the final gravitational potential energy

So: (7)

(8)

Where is the change in kinetic energy.

Hence:

(9) This is the change in kinetic energy

c) Isolating from (8):

(10)

Hence:

(11) This is the final kinetic energy of the projectile

d)These results will not change if we change the angle, since these equations do not depend on the angle.

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:

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles