Squids can move through the water using a form of jet propulsion. Suppose a squid jets forward from rest with constant acceleration for $0.170 \mathrm{~s}$, moving through a distance of $0.179 \mathrm{~m}$. The squid then turns off its jets and coasts to rest with constant acceleration. The total time for this motion (from rest to rest) is $0.400 \mathrm{~s}$, and the total distance covered is $0.421 \mathrm{~m}$. What is the time it coasts to a stop?

A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape for a given amount of fuel, should it fire its engines to accelerate forward when it is at the apogee or at the perigee? (Hint: Let the formula $F d=\Delta \mathrm{KE}$ be your guide to thinking. Suppose the thrust $F$ is brief and of the same duration in either case. Then consider the distance $d$ the rocket would travel during this brief burst at the apogee and at the perigee.)

Use the forward-difference formulas and backward-difference formulas to determine each missing entry in the following tables. a.

$$\begin{matrix} \text{x} & \text{f(x)} & f^{\prime}(x)\\ \text{0.5} & \text{ 0.4794 }\\ \text{0.6} & \text{ 0.5646 }\\ \text{0.7} & \text{ 0.6442}\\ \end{matrix}$$

b.

$$\begin{matrix} \text{x} & \text{f(x)} & f^{\prime}(x)\\ \text{0.0} & \text{ 0.00000 }\\ \text{0.2} & \text{ 0.74140 }\\ \text{0.4} & \text{1.3718 }\\ \end{matrix}$$

Albert is piloting his spaceship, heading east with a speed of $0.90 \mathrm{c}$. Albert's ship sends a light beam in the forward (eastward) direction, which travels away from his ship at a speed $c$. Meanwhile, Isaac is piloting his ship in the westward direction, also at $0.90 c$, toward Albert's ship. With what speed does Isaac see Albert's light beam pass his ship?

In a baseball game, a batter hits a ground ball 26 feet in the direction of the pitcher's mound. See the figure below. The pitcher runs forward and reaches for the ball. At that moment, how far is the ball from first base? (Note: A baseball infield is a square that measures 90 feet on each side.)

Complete the following sentences by choosing the word that best fits the context, based on information you infer from the use of the italicized word. Some word pairs will be antonyms, some will be synonyms, and some will simply be words often used in the same context. Ophelia exhorted her friends in their most _____ moments, compassionately urging them to move forward and to live life once again. A. pertinent, B. dolorous, C. gargantuan, D. grandiloquent, E. affable.

Squid use jet propulsion for rapid escapes. A squid pulls water into its body and then rapidly ejects the water backward to propel itself forward. A 1.5 kg squid (not including water mass) can accelerate at $20 \mathrm { m } / \mathrm { s } ^ { 2 }$ by ejecting 0.15 kg of water. a. What is the magnitude of the thrust force on the squid? b. What is the magnitude of the force on the water being ejected? c. What acceleration is experienced by the water?

Cargo is tied with rope on the roof of a 4.5-foot-tall car. The car is traveling down a road at 42 mph and hits a concrete barrier. The rope snaps, allowing the cargo to propel forward. Use the equations $y=-16.1 t^{2}+4.75$ and $y=-0.0042 x^{2}+4.75$ where y represents height in feet, x represents horizontal distance in feet, and t represents time in seconds, to find the time it takes for the cargo to hit the ground and the horizontal distance it travels.

The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is $1.80\ \mathrm{m} / \mathrm{s}^{2},$ what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion. For this situation, draw a free-body diagram and write the net force equation.

Given the equation representing a reversible reaction: $\mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{NH}_{4} \ ^{+}(a q)+\mathrm{OH}^{-}(a q)$ According to one add-base theory, the reactant that donates an $\mathrm{H}^{+}$ ion in the forward reaction is: (1) $\mathrm{H}_{2} \mathrm{O}(\ell)$ (2) $\mathrm{NH}_{3}(g)$ (3) $\mathrm{NH}_{4}^{+}(a q)$ (4) $\mathrm{OH}^{-}(a q)$.

When run at maximum power output, the motor in a self-propelled tank car can accelerate the full car (mass $M$ kg) along a horizontal track at $a$ m/s$^2$ . The tank is full at time zero, but the contents pour out of a hole in the bottom at rate $k$ kg/s thereafter. If the car is at rest at time zero and full forward power is turned on at that time , how fast will it be moving at any time $t$ before the tank is empty?

Ammonia gas dissolves in water according to the following equation:

$$\mathrm{NH}_3(g)+\mathrm{H}_2 \mathrm{O}(l) \rightleftarrows \mathrm{NH}_4^{+}(a q)+\mathrm{OH}^{-}(a q)+\text { energy; } K=1.8 \times 10^{-5}$$

______________a. Is aqueous ammonia an acid or a base?

______________b. Is the equation given above an example of hydrolysis?

______________c. For the given value of $K$, does the equilibrium favor the forward or reverse reaction?

The $K_{\mathrm{c}}$ at $100^{\circ} \mathrm{C}$ is $2.0$ for the decomposition reaction of NOBr. $2 \operatorname{NOBr}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{Br}_2(g)$ $In an experiment,$1.0$mole of$ $\mathrm{NOBr}$, 1.0$mole of$ $\mathrm{NO}, and$1.0$mole of$ $\mathrm{Br}$_2$were placed in a$1.0 $$ \mathrm{~L}$ container. c. If not, will the rate of the forward or reverse reaction initially speed up? $$

Consider a common mirage formed by superheated air immediately above a roadway. A truck driver whose eyes are 2.00 m above the road, where n = 1.000293, looks forward. She perceives the illusion of a patch of water ahead on the road. The road appears wet only beyond a point on the road at which her line of sight makes an angle of $1.20^{\circ}$ below the horizontal. Find the index of refraction of the air immediately above the road surface.