A tugboat pulls a small barge through a harbor. The propeller thrust minus the drag produces a net thrust that varies linearly with speed. Knowing that the combined weight of the tug and barge is 3600 kN, determine (a) the time required to increase the speed from an initial value $v_1$ = 1.0 m/s to a final value $v_2$ = 2.5 m/s, (b) the distance traveled during this time interval.

The coefficients of friction between the load and the flatbed trailer shown are $\mu_{s}=0.40$ and$\mu_{s}=0.30$. Knowing that the speed of the rig is 72 km/h, determine the shortest distance in which the rig can be brought to a stop if the load is not to shift.

A 5000-lb truck is being used to lift a 1000-lb boulder B that is on a 200-lb pallet A. Knowing the acceleration of the truck is 1 $\mathrm{ft} / \mathrm{s}^{2}$, determine (a) the horizontal force between the tires and the ground, (b) the force between the boulder and the pallet.

A $12-\mathrm{lb}$ block $B$ rests as shown on the upper surface of a $30-\mathrm{lb}$ wedge $A$. Neglecting friction, determine immediately after the system is released from rest $(a)$ the acceleration of $A,(b)$ the acceleration of $B$ relative to $A$.

Using a suitable angle of rotation for the conic with each given equation, write the equation in standard form. $145 x^{2}+120 x y+180 y^{2}=900$

A 0.2-lb model rocket is launched vertically from rest at time t = 0 with a constant thrust of 2 lb for one second and no thrust for t > 1 s. Neglecting air resistance and the decrease in mass of the rocket, determine (a) the maximum height h reached by the rocket, (b) the time required to reach this maximum height.

As part of an outdoor display, a $5 \mathrm{~kg}$ model $C$ of the earth is attached to wires $A C$ and $B C$ and revolves at a constant speed $v$ in the horizontal circle shown. Determine the range of the allowable values of $v$ if both wires are to remain taut and if the tension in either of the wires is not to exceed $116 \mathrm{~N}$.

Using only a periodic table, predict the ground state 18-outer electron configuration and the charge of a (a) cadmium ion (b) indium(III) ion (c) zinc ion (d) thallium(III) ion

Determine the whole for the percent and part given. 68 is 32% of what number?

A loading car is at rest on a track forming an angle of $25^{\circ}$ with the vertical. The gross weight of the car and its load is $5500 \mathrm{~lb}$, and it acts at point $G$. Knowing the tension in the cable connected at $C$ is $3000 \mathrm{~lb}$, determine $(a)$ the acceleration of the car, $(b)$ the reaction at each pair of wheels.

The value of $g$ at any latitude $\phi$ may be obtained from the formula

$$g=32.09\left(1+0.0053 \sin ^2 \phi\right) f \mathrm{f} / \mathrm{s}^2$$

which takes into account the effect of the rotation of the earth, as well as the fact that the earth is not truly spherical. Knowing that the weight of a silver bar has been officially designated as $5 \mathrm{~lb}$, determine to four significant figures $(a)$ the mass in slugs, $(b)$ the weight in pounds at latitudes of $0^{\circ}$, $30^{\circ}$, and $50^{\circ}$.

Use the remainder theorem to determine the remainder of each division. a) $6 x^{3}-7 x^{2}+5 x+8$ divided by x - 2 b) $3 x^{4}+x^{3}-2 x+1$ divided by 3x + 4

Find the partial fraction decomposition of each rational expression with prime quadratic factors in the denominator. $\frac{4 x^{4}+x^{2}-25 x+32}{x^{5}-4 x^{3}+4 x}$

The robot arm is elevating and extending simultaneously. At a given instant $\theta=30^{\circ}, \dot{\theta}=10 \operatorname{deg} / \mathrm{s}$, Compute the magnitudes of the velocity v and acceleration a of the gripped part P. In addition, express v and a in terms of the unit vectors i and j. $\text { constant, } l=0.5 m, \dot{l}=0.2 m/s, \text { and } \ddot{l}=-0.3 \mathrm{m}/s^{2}$.