A $62-\mathrm{kg}$ skier starts from rest at the top of a ski jump, point $\mathrm{A}$ in given Fig, and travels down the ramp. If friction and air resistance can be neglected, find her speed $v_{\mathrm{B}}$ when she reaches the horizontal end of the ramp at B.

At the instant it leaves the player's hand after a jump shot, a $0.62$-$\mathrm{kg}$ basketball is traveling $8.4 \mathrm{~m} / \mathrm{s}$. When it passes through the hoop its speed is $6.8 \mathrm{~m} / \mathrm{s}$. How much work has gravity done on the ball?

A long jumper approaches his takeoff board $A$ with a horizontal velocity of $30 \mathrm{ft} / \mathrm{sec}$. Determine the vertical component $v_y$ of the velocity of his center of gravity at takeoff for him to make the jump shown. What is the vertical rise $h$ of his center of gravity?

To be rescued from the roof of a burning building, a 70-kg man must be able to jump straight up and catch hold of a rope ladder hanging from a helicopter. He has to raise his center of mass 2.00 m above the roof to do so. (a) If he crouches down such that his center of mass is 0.50 m above the roof and his feet leave the roof when his center of mass is 1.05 m above the roof, what minimum force must he exert on the roof to reach the ladder? (b) A typical candy bar contains about 850 kJ of food energy. How many candy bars does this jump require?

The energy gap $E_{\mathrm{g}}$ in germanium is 0.72 eV. When used as a photon detector, roughly how many electrons can be made to jump from the valence to the conduction band by the passage of a 760-keV photon that loses all its energy in this fashion?

Determine whether each function is continuous at the given x-value(s). Justify using the continuity test. If discontinuous, identify the type of discontinuity as infinite jump, or removable.

$$f(x)=\left\{\begin{array}{rl} {3 x-1} & {\text { if } x<1} \\ {2 x} & {\text { if } x \geq 1} \end{array} ; x=1\right.$$

A banquette table at your restaurant measures 30 inches wide and 42 inches long. What is the perimeter of this table? What is the perimeter if two tables are pushed together to form a double-length table?

(II) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground to lift his center of mass $2.10\ \text{m}$ and cross the bar with a speed of $0.50\ \text{m/s}$?

A diver jumps from a 40.0-m-high cliff into the sea. Rocks stick out of the water for a horizontal distance of 7.00 m from the foot of the cliff. With what minimum horizontal speed must the diver jump off the cliff in order to clear the rocks and land safely in the sea?

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table. $\int \frac{\cos x}{\sin ^{2} x+2 \sin x} d x$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table. $\int \frac{e^{x}}{\sqrt{e^{2 x}-4}} d x$

Sketch the graph and classify the discontinuities (if any) as being removable or essential. If the latter, is it a jump discontinuity, an infinite discontinuity, or neither. \

$$f(x)=\left\{\begin{aligned}-1, \quad & x<-1 \\ x^3, \quad &-1 \leq x \leq 1 \\ 1, \quad & 1<x. \end{aligned}\right.$$

Louis recorded how many times he could jump rope without stopping. Here is his data: 50 15 102 64 29 55 100 97 48 81 61 Find the median, first quartile, and third quartile of his data.

In a world without friction, which of the following activities could you do (or not do)? Explain your reasoning. (a) drive around an unbaked highway curve; (b) jump into the air; (c) start walking on a horizontal sidewalk; (d) climb a vertical ladder; (c) change lanes on the freeway.