A 57.0-kg boy and his 43.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.00 m/s toward the west. Ignore friction.(a) Describe the subsequent motion of the girl. (b) How much potential energy in the girls body is converted into mechanical energy of the boy-girl system? (c) Is the momentum of the boy-girl system conserved in the pushing-apart process? If so, explain how that is possible considering (d) there are large forces acting and (e) there is no motion beforehand and plenty of motion afterward.

a) Since linear momentum IS conserved, the momentum of the girl is actually -4.7125*43 = -202.6 kg∙ m/s (opposite direction from the boy).

When this is added to the boy's momentum (+202.6), the result is zero.

This is expected since the initial momentum is also zero.  

b)  733.97 J  potential energy in the girls body is converted into mechanical energy of the boy-girl system

c) YES the momentum of the boy-girl system conserved in the pushing-apart process because the velocities (vectors) are opposite and the individual momentum therefore cancel leaving zero, the same as before the pushing.

Explanation:

b) ME = KE = ½ΣMV² = ½(57*3.0² + 43*4.7125²) = 733.97 J

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft