In firefighting, a good water stream can be modeled by y = -0.003x$^2$ + 0.62x + 3
where x is the water’s horizontal distance traveled (in feet) and y is its corresponding height (in feet). If a firefighter is aiming a good water stream at a building’s window 25 feet above the ground, at what two distances can the firefighter stand from the building?

Write the quadratic function in standard form.
y = 5(x + 6)$^2$ - 12

A speed ramp at an airport is basically a large conveyor belt on which you can stand and be moved along. The belt of one ramp moves at a constant speed such that a person who stands still on it leaves the ramp 64 s after getting on. Clifford is in a real hurry, however, and skips the speed ramp. Starting from rest with an acceleration of

$$0.37 m/s^2,$$

he covers the same distance as the ramp does, but in one-fourth the time. What is the speed at which the belt of the ramp is moving?

A race driver has made a pit stop to refuel. After refueling, he leaves the pit area with an acceleration whose magnitude is

$$6.0 \mathrm { m } / \mathrm { s } ^ { 2 }$$

after 4.0 she enters the main speedway. At the same instant, another car on the speedway and traveling at a constant speed of 70.0 m/s overtakes and passes the entering car. If the entering car maintains its acceleration, how much time is required for it to catch the other car?

Two cars cover the same distance in a straight line. Car A covers the distance at a constant velocity Car B starts from rest, maintains a constant acceleration, and covers the distance in the same time as car A. (a) Is car B's final velocity smaller than, equal to, or greater than car A's constant velocity? Explain. (b) Is car B's average velocity smaller than, equal to, or greater than car A's constant velocity? Why? (c) Given a value for the time to cover the distance and the fact that car B starts from rest, what other variable must be known before car B's acceleration can be determined? Provide a reason for your answer. Both cars cover a distance of 460 m in 210 s. Assume that they are moving in the +x direction. Determine (a) the constant velocity of car A, (b) the final velocity of car B, and (c) the acceleration of car B.

A cheetah is hunting. Its prey runs for 3.0 s at a constant velocity of +9.0 m/s. Starting from rest, what constant acceleration must the cheetah maintain in order to run the same distance as its prey runs in the same time?

A jogger accelerates from rest to 3.0 m/s in 2.0 s. A car accelerates from 38.0 to 41.0 m/s also in 2.0 s. (a) Find the acceleration (magnitude only) of the jogger. (b) Determine the acceleration (magnitude only) of the car. (c) Does the car travel farther than the jogger during the 2.0 s? If so, how much farther

The left ventricle of the heart accelerates blood from rest to a velocity of +26 cm/s.

If the displacement of the blood during the acceleration is +2. 0 cm, determine its acceleration $\left( \text { in } \mathrm { cm } / \mathrm { s } ^ { 2 } \right)$

Solve the inequality. Then graph your solution.
$\frac3 2$x+ 20 $\leq$ 14 or 1 > 8 - x

A whale swims due east for a distance of 6.9 km, turns around and goes due west for 1.8 km, and finally turns around again and heads 3.7 km due east. What is the total distance traveled by the whale?

In 1998, NASA launched Deep Space 1 (DS-1), a spacecraft that successfully flew by the asteroid named 1992 KD (which orbits the sun millions of miles from the earth). The propulsion system of DS-1 worked by ejecting high-speed argon ions out the rear of the engine. The engine slowly increased the velocity of DS-1 by about +9.0 m/s per day. (a) How much time (in days) would it take to increase the velocity of DS-1 by +2700 m/s? (b) What was the acceleration of DS-1 (in $\mathrm{m} / \mathrm{s}^{2}$)?

Over a time interval of 2.16 years, the velocity of a planet orbiting a distant star reverses direction, changing from +20.9 km/s to - 18.5 km/s. Find

the total change in the planet's velocity (in m/s)

Jackie Joyner-Kersee won the women’s heptathlon during the 1992 Olympics in Barcelona, Spain. Her throw in the shot put, one of the seven events in the heptathlon, can be modeled by y = -0.0241x$^2$ + x + 5.5
where x is the shot put’s horizontal distance traveled (in feet) and y is its corresponding height (in feet). How long was Joyner-Kersee’s throw?

In 1954 the English runner Roger Bannister broke the four-minute barrier for the mile with a time of 3:59.4 s (3 min and 59.4 s). In 1999 the Moroccan runner Hicham el-Guerrouj set a record of 3:43.13 s for the mile. If these two runners had run in the same race, each running the entire race at the average speed that earned him a place in the record books, el-Guerrouj would have won. By how many meters?