Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

The band's crescendo at the end of their hit song...

A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in t seconds is given by the function $d(t)=16 t^{2} \mathrm{ft}$ (a) After how many seconds will the diver hit the water? (b) With what velocity does the diver hit the water?

use the formula

$$h(t) = v_0t -16t^2,$$

where h(t) is the height of an object in feet,

$$v_0$$

is the object's initial velocity in feet per second, and t is the time in seconds. A golf ball is hit with an initial velocity of 100 feet per second. How long will it take for it to hit the ground?

Alana plays softball for Centerville High School. So far this season she lias gotten a hit 4 out of 12 times at bat. She is determined to improve her batting average. If she can get x consecutive hits, her batting average can be determined using

$$B ( x ) = \frac { 4 + x } { 12 + x }$$

What part of the graph is meaningful in the context of the problem?

A tennis player is practicing her serve. She aims for a can placed 57 feet from her in the service box. If she hits the ball when it is 9 feet in the air, what angle must the path of the ball make with the ground in order for the ball to hit the can’s base? Assume the ball travels along a straight line. Explain your answer.

A ball is thrown downward with a speed of 8 ft/s from the top of a 64-foot-tall building. After t seconds, its height above the ground is given by $s(t)=-16 t^{2}-8 t+64$. a. Determine how long it takes for the ball to hit the ground. b. Determine the velocity of the ball when it hits the ground.

When Babe Ruth hit a homer over the $8.0\,\text{m}$ high right-field fence $98 \mathrm{~m}$ from home plate, roughly what was the minimum speed of the baseball when it left the bat? Assume the ball was hit $1.0 \mathrm{~m}$ above the ground and its path initially made a $36^{\circ}$ angle with the ground.

A $0.35-\mathrm{kg}$ tennis racquet moving to the right at $20.0 \mathrm{~m} / \mathrm{s}$ hits a $0.060-\mathrm{kg}$ tennis ball that is moving to the left at $30.0 \mathrm{~m} / \mathrm{s}$. The racquet continues moving to the right after the collision but at a reduced speed of $10.0 \mathrm{~m} / \mathrm{s}$. What is the velocity of the tennis ball after it is hit by the racquet?

Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire at the same time, but each chooses his target at random, independently of the others. If each hunter independently hits his target with probability .6, compute the expected number of ducks that are hit. Assume that the number of ducks in a flock is a Poisson random variable with mean 6.

A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle $\theta$ to the horizontal is given by $R(\theta)=672 \sin (2 \theta),$ where R is measured in feet. At what angle $\theta$ should the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)?

You throw a ball straight up into the air at $18 \mathrm{~m} / \mathrm{s}$ from a height of $32 \mathrm{~m}$ above the ground. (a) Calculate the time the ball takes to hit the ground. (b) Calculate the velocity of the ball when it hits the ground. (c) Calculate the maximum height of the ball. (d) Explain why you cannot use half the time for (a) to answer (c).

Roberto wants to know the expected number of at-bats until he gets a hit. What would you tell him?

Alana plays softball for Centerville High School. So far this season she has gotten a hit 4 out of 12 times at bat. She is determined to improve her batting average. If she can get x consecutive hits, her batting average can be determined using

$$B ( x ) = \frac { 4 + x } { 12 + x }$$

Describe the meaning of the intercept of the vertical axis.

Apollo astronauts took a "nine iron" to the Moon and hit a golf ball about $180$ m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only $30$ m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!)