After the sun exhausts its nuclear fuel, its ultimate fate will be to collapse to a white dwarf state. in this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the earth.

(a) calculate the average density of the white dwarf.
kg/m3

(b) calculate the surface free-fall acceleration.
m/s2

(c) calculate the gravitational potential energy associated with a 3.91-kg object at the surface of the white dwarf.
j

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?