At a given instant t(0), a 1000kg earth orbiting satellite has the inertial position and velocity vectors, r(0) = 3207i + 5459j + 2714k (km) and v(0) = -6.532i + 0.7835j + 6.142k (km/s). solve eq 2.22 numerically to fin the maximum altitude reached by the satellite and the time at which it occurs.

equation 2.22: r'' = -(u/r^3)(r)

u = gravitational parameter = g(m1 + m2)

r = position vector

(ans: using matlab's ode45 function, distance = 456,500km, speed = 5km/s.)

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

Aperson gives a shopping cart an initial push along a horizontal floor to get it moving, and then lets go. the cart travels forward along the floor, gradually slowing as it moves. consider the horizontal force(s) on the cart while it is moving forward and slowing. which of the following statements is correct? (a) both a forward and a backward force are acting on the cart, but the forward force is larger. (b) only a forward force is acting which diminishes with time. (c) both a forward and a backward force are acting on the cart, but the backward force is larger. (d) only a backward force is acting, no forward force.

On your wedding day your lover gives you a gold ring of mass 3.67 g. 48 years later its mass is 3.44 g. on the average how many atoms were abrated from the ring during each second of your marriage? the atomic mass of gold is 197 u. don't enter units