P6 done 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. The height is s feet, t represents the time in seconds, vo is the initial velocity in feet per second, and so is the initial height in feet. 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.
acceleration: 32 ft/s2, initial velocity: 56 ft/s, initial height: 35 ft
- Each year the Punkin’ Chunkin’ contest is held in Lewes, Delaware. The object of the contest is to propel an 8- to 10-pound pumpkin as far as possible. Steve Young of Hopewell, Illinois, set the 1998 record of 4026.32 feet. 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?
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 − 𝑔𝑡 , where vo is the initial velocity and g represents the d(t) acceleration due to gravity. The acceleration due to gravity is 32 feet per second squared.
How long will it take the stuntwoman to reach the safety pad on the ground?
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. The vertical distance from the top of the hill to the bottom of the hill is 25 meters.
5 secs
- When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance driven divided by the total time spent driving. A trucker drove 3 hours on a freeway at 60 miles per hour and then drove 20 miles in the city. The trucker’s average speed was 57.14 miles per hour. How long was the trucker driving in the city to the nearest hundredth of an hour?
0.5 h
The diagram of an electric circuit shows three parallel resistors. If R represents the equivalent resistance of the three resistors ………….
A. Write a rational equation to model the situation
(1/10)= (1/2r) + (1/r) + (1/20)
The diagram of an electric circuit shows three parallel resistors. If R represents the equivalent resistance of the three resistors ………….
B. Find R1 and R2
60 ohmns, 30 ohms
- The velocity of a roller coaster as it moves down a hill is 𝑣 = √𝑣2 + 64ℎ, where v0 is the initial velocity and h is the vertical drop in feet. The designer of a coaster wants the coaster to have a velocity of 90 feet per second when it reaches the bottom of the hill.
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.
90 = √100 + 64ℎ
- The velocity of a roller coaster as it moves down a hill is 𝑣 = √𝑣2 + 64ℎ, where v0 is the initial velocity and h is the vertical drop in feet. The designer of a coaster wants the coaster to have a velocity of 90 feet per second when it reaches the bottom of the hill.
B. How high should the designer make the hill?
125 ft
- The period of a pendulum (the time required for one back and forth swing) can be determined by the formula 𝑙 . In this formula, T represents 𝐺 the period, l represents the length of the pendulum, and g represents acceleration due to gravity.
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.
2.01 s
- The period of a pendulum (the time required for one back and forth swing) can be determined by the formula 𝑙 . In this formula, T represents 𝐺 the period, l represents the length of the pendulum, and g represents acceleration due to gravity.
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.
2.11s
- The period of a pendulum (the time required for one back and forth swing) can be determined by the formula 𝑙 . In this formula, T represents 𝐺 the period, l represents the length of the pendulum, and g represents acceleration due to gravity.
c. How must the length of the pendulum be changed to double the period?
multiplied by 4
- 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°
- Biking During the winter, a competitive bike rider trains on a stationary bike. Her trainer wants her to warm up for 5 to 10 minutes by pedaling slowly. Then she is to increase the pace to 95 revolutions per minute for 30 seconds. Through how many degrees will a point on the outside of the tire travel during the 30 seconds of the faster pace?
17,100
- 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. Suppose vertically polarized light with intensity Io strikes a polarized filter with its axis at an angle of with the vertical. The intensity of the transmitted light It and are related by the equation cos𝜃 = 𝐼𝑡 . 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 emasure of an angle of refraction is 27
1.5103
- When rounding a curve, the acute angle that a runner’s body makes withthe vertical is called the angle of incline. It is described by the equation tan 𝜃 = 𝑣2 , where v is the velocity of the runner, g is the acceleration due to 𝑔𝑟 gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters.
a. What is the runner’s velocity if the angle of incline is 11°?
5.4 m/s
- 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 equation tan 𝜃 = 𝑣2 , where v is the velocity of the runner, g is the acceleration due to 𝑔𝑟 gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters.
b. What is the runner’s velocity if the angle of incline is 13°?
5.9 m/s
- 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 equation tan 𝜃 = 𝑣2 , where v is the velocity of the runner, g is the acceleration due to 𝑔𝑟 gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters.
c. What is the runner’s velocity if the angle of incline is 15°?
6.4 m/s
- 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 equation tan 𝜃 = 𝑣2 , where v is the velocity of the runner, g is the acceleration due to 𝑔𝑟 gravity, and r is the radius of the track. The acceleration due to gravity is a constant 9.8 meters per second squared. Suppose the radius of the track is 15.5 meters.
d. should a runner increase or decrease her velociy t increase his or her angle of incmline
increase
- Highway curves are usually banked or tilted inward so that cars can negotiate the curve more safely. The proper banking angle for a car making a turn of radius r feet at a velocity of v feet per second is given by the equation is tan 𝜃 = 𝑣2 . In this equation, g is the acceleration due to gravity or 32 feet 𝑔𝑟 per second squared. 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?
about 13.3
A steel beam is supported by two pilings 200 feet part. if a weight is placed x feet from the piling on the left, a vertical deflection d equals 0.00000008
100ft
