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 uniform slender bar has an ideal roller at its upper end A. Determine the minimum value of the angle $\theta$ for which equilibrium is possible for $\mu_{s}=0.25$ and for $\mu_{s}=0.50$.

The light bar is used to support the 50 kg block in its vertical guides. If the coefficient of static friction is 0.30 at the upper end of the bar and 0.40 at the lower end of the bar, find the friction force acting at each end for x=75mm. Also find the maximum value of x for which the bar will not slip.

In a drama club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the drama club at an arts symposium?

A boy of mass 60.0 kg is rescued from a hotel fire by leaping into a firefighters' net. The window from which he leapt was 8.0 m above the net. The firefighters lower their arms as he lands in the net so that he is brought to a complete stop in a time of 0.40 s. (a) What is his change in momentum during the 0.40 s interval? (b) What is the impulse on the net due to the boy during the interval? [Him: Do not ignore gravity.] (c) What is the average force on the net due to the boy during the interval?

Some water is placed in a coffee cup calorimeter. When 1.0 g of an ionic solid is added, the temperature of the solution increases from $21.5 ^ { \circ } \mathrm { C }$ to $24.2 ^ { \circ } \mathrm { C }$ as the solid dissolves. For the dissolving process, what are the signs for $\Delta S _ {sys}, \Delta S _ {surr},$ and $\Delta S _ {univ}?$

A box slides across a frozen pond toward the left shore as two children standing on opposite shores pull on the box with ropes. The child on the left shore pulls with a force of 3.0 N, and the child on the right shore pulls with a force of 2.0 N. At a certain instant, the speed of the box is 3.0 m/s. (a) At that instant, what is the power resulting from each force? (b) What is the power resulting from both forces? (c) Do your answers to parts a and b change as the box slides?

Let P(x) be the cumulative distribution function for the household income distribution in the US in 2009. Values of P(x) are in the following table:

Income x (thousand $): 20, 40, 60, 75, 100 P(x) (%): 29.5, 50.1, 66.8, 76.2, 87.1

Is the statement "More than one-third of households made between$40,000 and $75,000" true or false?

Sandra is a 25-year old woman who weighs 120 lb. She burns 300 − 50t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 100t calories during the tth hour. What is her net decrease in calories after walking for 3 hours?

If a function f has no limit as x approaches c, then we say that $\lim _{x \rightarrow c} f(x)$ _____ _____ _____.

The following list of prices is for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio. $210,$210, $320,$200, $300,$10, $340,$300, $245,$325, $700,$250, $240,$200 Find the four quartiles.

Use synthetic division to find each quotient. $\frac{y^{3}+1}{y-1}$

Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.

$$0.75 x ^ { 2 } + 1.5 x = 4$$

Why is it important for everyone, even good swimmers, to know the technique of survival floating?