GLEN-P6 Flashcards
- The height of an object that is thrown upward with a constant acceleration
of a feet per second per second is given by the equation s = ½ at^2 + vt + s. Find the acceleration, the
initial velocity, and the initial height if the height at 1 second is 75 feet, the
height at 2.5 seconds is 75 feet, and the height at 4 seconds is 3 feet.
ANS: acceleration: 32 ft/s2, initial velocity: 56 ft/s, initial height: 35 ft
- Each year the Punkin’ Chunkin’ contest is held in Lewes, Delaware. Suppose you build a machine that fires the pumpkin so that it is at a height of
124 feet after 1 second, the height at 3 seconds is 272 feet, and the height at
8 seconds is 82 feet.
ANS: (32, 138, 2)
When the position of a particle as a function of time t is modeled by a
polynomial function, then the particle is at rest at each critical point. If a particle
has a position given by 𝑠(𝑡) = 2𝑡3 − 11𝑡2 + 3𝑡 − 9, find the position of the particle each time it is at rest.
ANS: The particle is at rest when t = 0.14 and when t = 3.52.
Its positions at these times are s (0.14) = -8.79 and s (3.52) = -47.51
- On a cold day, a 12-volt car battery has a resistance of 0.02 ohms. The
power available to start the motor is modeled by the equation P = 12I + 0.02I^2,
where I is the current in amperes. What current is needed to produce 1600
watts of power to start the motor?
ANS: 200 or 400 amps
- In an action movie, a stuntwoman jumps off a building that is 50 feet tall with
an upward initial velocity of 5 feet per second. The distance d(t) traveled by a
free-falling object can be modeled by the formula 𝑑(𝑡) = 𝑣𝑜𝑡 −1/2𝑔𝑡2,How long will it take the stuntwoman to reach the safety pad on the ground?
ANS: about 1.93 s
- Matthew is cycling at a speed of 4 meters per second. When he starts down
a hill, the bike accelerates at a rate of 0.4 meter per second squared.
ANS: 5 secs
- When truckers are on long-haul drives, their driving logs must reflect their
average speed. How long was the trucker driving in the city to the nearest
hundredth of an hour?
ANS: 0.50 h
- The diagram of an electric circuit shows three parallel resistors. If R
represents the equivalent resistance of the three resistors,then 1/𝑅 = 1/𝑅1+1/𝑅2+1/𝑅3,
A. Write a rational equation to model the situation.
ANS: 1/10=1/2𝑟+1/𝑟+1/20
B. Find R1 and R2.
ANS: 60 ohms, 30 ohms
- The velocity of a roller coaster as it moves down a hill is 𝑣 = √𝑣𝑜2 + 64ℎ,
A. If the initial velocity of the coaster at the top of the hill is 10 feet per second,
write an equation that models the situation.
ANS: 90 = √100 + 64ℎ
B. How high should the designer make the hill?
ANS: 125 ft
- The period of a pendulum (the time required for one back and forth swing)
a. Determine the period of a 1-meter pendulum on Earth if the acceleration
due to gravity at Earth’s surface is 9.8 meters per second squared.
ANS: about 2.01 s
b. Suppose the acceleration due to gravity on the surface of Venus is 8.9
meters per second squared. Calculate the period of the pendulum on Venus.
ANS: about 2.11 s
- A computer’s hard disk is spinning at 12.5 revolutions per second. Through
how many degrees does it travel in a second? in a minute?
ANS: 4500°; 270,000°
- You may have polarized sunglasses that eliminate glare by polarizing the
light. When light is polarized, all of the waves are traveling in parallel planes. cos𝜃 = √𝐼𝑡/𝐼𝑜. Write It as a function of Io.
ANS: It = 0.5Io
- Suppose a ray of light passes from air to Lucite. The measure of the angle
of incidence is 45°, and the measure of an angle of refraction is 27° 55’. Use
Snell’s Law to find the index of refraction for Lucite.
ANS: about 1.5103
- When rounding a curve, the acute angle that a runner’s body makes with
the vertical is called the angle of incline. It is described by the equationtan 𝜃 =𝑣²/𝑔𝑟,
a. What is the runner’s velocity if the angle of incline is 11°?
ANS: 5.4 m/s
b. Find the runner’s velocity if the angle of incline is 13°?
ANS: 5.9 m/s
c. What is the runner’s velocity if the angle of incline is 15°?
ANS: 6.4 m/s
d. Should a runner increase or decrease her velocity to increase his or her
angle of incline?
ANS: increase
- Highway curves are usually banked or tilted inward so that cars can
negotiate the curve more safely. An engineer is designing a curve with a radius of 1200
feet. If the speed limit on the curve will be 65 miles per hour, at what angle
should the curve be banked?
ANS: about 13.3°
- A steel beam is supported by two pilings 200 feet apart. If a weight is placed
x feet from the piling on the left, a vertical deflection d equals
0.0000008x^2(200 - x). How far is the weight if the vertical deflection is 0.8
feet?
ANS: 100 ft
c. How must the length of the pendulum be changed to double the period?
ANS: It must be multiplied by 4.
