Explain why sound travels faster through some types of matter than through others. How does temperature affect the speed of sound through a material?

A wooden block of mass $M$ rests on a table over a large hole as we discussed earlier. A bullet of mass $m$ with an initial velocity of $v_i$ is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of $h$.
(b) Find an expression for the initial velocity of the bullet.

Explain why sound travels faster through some types of matter than through others. How does temperature affect the speed of sound through a material?

Graph the line passing through the given point with the given slope.

Through $(-2,0)$ with slope $-3$

You’re driving along at 25 m / s with your aunt’s valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road 55 m ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero! a. Can you stop the truck before it falls into the hole? b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are $\mu_{\mathrm{s}}=0.60 \text { and } \mu_{\mathrm{k}}=0.30$. Hint: You’re not trying to stop in the shortest possible distance. What’s your best strategy for avoiding damage to the antiques?

A 12 h water clock is to be designed with the dimensions, shaped like the surface obtained by revolving the curve y = f(x) around the y-axis. What should this curve be, and what should the radius of the circular bottom hole be, in order that the water level will fall at the constant rate of 4 inches per hour (in./h)?

Determine the equation of the parabola with vertex a) (-2, 5) and that passes through (4, -8) b) (1, 6) and that passes through (0, -7) c) (4, -5) and that passes through (-1, -3) d) (4, 0) and that passes through (11, 8)

How many bits per word are needed to represent the decimal integers 0 through 100? 0 through 1000? 0 through $10^6?$

One of the CFCs that is implicated in decreasing the ozone layer and formation of the ozone hole over Antarctica is Freon-12 or $\mathrm{CCl_2F_2}$. Calculate the density of Freon-12 at STP and compare it to the average density of air. Suggest how Freon-12 can get into the stratosphere to threaten the ozone layer.

Why does sound travel faster through water than through air?

Determine an equation of the plane through $(-2,3,4)$ and perpendicular to the line through $(4,-2,5)$ and $(0,2,4)$.

Determine the equation of a line for the given information.

(a). slope $4, y$-intercept $-2$ (b). slope $-2, y$-intercept $5$ ($c$). through $(-1,6)$ and $(4,12)$ (d). through $(-2,4)$ and $(-6,8)$ (e). vertical, through $(-3,5)$ (f). horizontal, through $(-3,5)$

Determine the equation of each line.

a) passes through $(1,1)$ and $(-3,4)$

b) passes through $(5,8)$ and $(6,6)$

(a) A solid compound of molar mass $100\ \mathrm{g}\ \mathrm{mol}^{-1}$ was introduced into a container and heated to $400^{\circ} \mathrm{C}.$ When a hole of diameter 0.50 nm was opened in the container for 400 s, a mass loss of 285 mg was measured. Calculate the vapour pressure of the compound at $400^{\circ} \mathrm{C}.$ (b) A solid compound of molar mass $200\ \mathrm{g}\ \mathrm{mol}^{-1}$ was introduced into a container and heated to $300^{\circ} \mathrm{C}.$ When a hole of diameter 0.50 nm was opened in the container for 500 s, a mass loss of 277 mg was measured. Calculate the vapour pressure of the compound at $300^{\circ} \mathrm{C}.$