The $160-\mathrm{Mg}$ train travels with a speed of $80 \mathrm{~km} / \mathrm{h}$ when it starts to climb the slope $\left(\tan\theta = \frac{1}{10}\right)$. If the engine exerts a traction force $\mathbf{F}$ of $1 / 20$ of the weight of the train and the rolling resistance $\mathbf{F}_D$ is equal to $1 / 500$ of the weight of the train, determine the deceleration of the train.

The man pushes on the $60\text{-lb}$ crate with a force $\mathbf{F}$. The force is always directed down at $30^{\circ}$ from the horizontal, and its magnitude is increased until the crate begins to slide. Determine the crate's initial acceleration if the coefficient of static friction is $\mu_s=0.6$ and the coefficient of kinetic friction is $\mu_k=0.3$.

Determine the constant speed of satellite S so that it circles the earth with an orbit of radius r = 15 Mm.

A communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the rotation of the earth, which is approximately 24 hours. Determine the satellite’s altitude h above the earth’s surface and its orbital speed.

A satellite is launched with an initial velocity $v_0=4000 \mathrm{~km} / \mathrm{h}$ parallel to the surface of the earth. Determine the required altitude (or range of altitudes) above the earth's surface for launching if the free-flight trajectory is to be (a) circular, (b) parabolic, $(c)$ elliptical, and (d) hyperbolic.