Why do tires grip the road better on level ground than they do when going uphill or downhill?

A $110$-kg man lowers himself to the ground from a height of $12$ m by holding on to a rope passed over a frictionless pulley and attached to a $74$-kg sandbag. $(a)$ With what speed does the man hit the ground? $(b)$ Is there anything he could do to reduce the speed with which he hits the ground?

A particle of mass $m$ is subjected to a net force $\overrightarrow{\mathbf{F}}(t)$ given by $\overrightarrow{\mathbf{F}}(t)=F_0(1-t / T) \hat{\mathbf{i}}$; that is, $F(t)$ equals $F_0$ at $t=0$ and de- creases linearly to zero in time $T$. The particle passes the ori- gin $x=0$ with velocity $v_0 \hat{\mathbf{i}}$. Show that at the instant $t=T$ that $F(t)$ vanishes, the speed $v$ and distance $x$ traveled are given by $v(T)=v_0+a_0 T / 2$, and $x(T)=v_0 T+a_0 T^2 / 3$, where $a_0=F_0 / m$ is the initial acceleration. Compare these results with earlier Eqs.

The position of a particle of mass $2.17$ kg traveling in a straight line is given by

$$x=\left(0.179 \mathrm{~m} / \mathrm{s}^4\right) t^4-\left(2.08 \mathrm{~m} / \mathrm{s}^2\right) t^2+17.1 \mathrm{~m} .$$

Find the $(a)$ velocity, $(b)$ acceleration, and $(c)$ force on the particle at time $t=7.18$ s.

Assume that the standard kilogram would weigh exactly $9.80$ N at sea level on the equator if the Earth did not rotate. Then take into account the fact that the Earth does rotate, so that this object moves in a circle of radius $6370$ km (the Earth’s radius) in one day. $(a)$ Determine the centripetal force needed to keep the standard kilogram moving in its circular path. $(b)$ Find the force exerted by the standard kilogram on a spring balance from which it is suspended at the equator (its apparent weight).

A model airplane of mass $0.75$ kg is flying at constant speed in a horizontal circle at one end of a $33$-m cord and at a height of $18$ m. The other end of the cord is tethered to the ground. The airplane makes $4.4$ rev/min and the lift is perpendicular to the unbanked wings. $(a)$ What is the acceleration of the plane? $(b)$ What is the tension in the cord? $(c)$ What is the lift produced by the plane’s wings?

A frigate bird is soaring in a horizontal circular path. Its bank angle is estimated to be $25\degree$ and it takes $13$ s for the bird to complete one circle. $(a)$ How fast is the bird flying? $(b)$ What is the radius of the circle? (See “The Amateur Scientist” by Jearl Walker, $\it{Scientific~ American}$, March $1985$, p. $122$.)

An insurance company estimated that $30 \%$ of all automobile accidents were partly caused by weather conditions and that $20 \%$ of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by weather conditions.

What is the probability that a randomly chosen accident both was partly caused by weather conditions and involved bodily injury?

Are the events "partly caused by weather conditions" and "involved bodily injury" independent?

If a randomly chosen accident was partly caused by weather conditions, what is the probability that it involved bodily injury?

What is the probability that a randomly chosen accident both was not partly caused by weather conditions and did not involve bodily injury?

Weather A scientist hopes to launch a weather balloon on one of the next three mornings. For each morning, there is a 40% chance of suitable weather. What is the probability that there will be at least one morning with suitable weather? Understanding the Problem What is the problem asking you to determine?

Larry shared his baseball cap collection equally among 8 friends. Each friend received 15 caps. How many caps did Larry give away?

A boat's capacity plate gives the maximum weight and/or number of people the boat can carry safely in certain weather conditions. What are these conditions?

a. rainy weather

b. weather with winds up to 76 knots

c. weather with winds up to 154 knots

d. good weather

What are the six atmospheric conditions that make weather?

What are the average weather conditions affecting a biome called?

Construct the tree o.f the algebraic expression.

$$(11-(11 \times(11+11)))+(11+(11 \times 11))$$