AFM Name______
Wkst 1
Quadratics
1. A meteorologist sends a temperature probe on a small weather rocket through a cloud layer. The launch pad for the rocket is 2 feet off the ground. The height of the rocket after launching is modeled by the equation, where is the height of the rocket in feet and t is the elapsed time in seconds.
a) What is the initial height of the rocket?
b) What is the initial velocity of the rocket?
c) When will the rocket be 114 ft above the ground?
d) What is the maximum height that the rocket reaches?
e) How long does it take to reach that maximum height?
f) From the time that it is launched, how long does it take for the rocket to hit the ground?
2. At liftoff, the space shuttle Discovery has a constant acceleration, a, of 16.4 ft/sec2. The function can be used to determine the distance from Earth for each time interval, t, after takeoff.
a) Find the distance from Earth after 30 seconds.
b) Find the distance from Earth after 2 minutes.
3. Normal systolic blood pressure is a function of age. For a woman the normal systolic pressure, P, in mm of mercury (mm Hg) is modeled by, where A is age in years.
a) Find the normal systolic pressure of a 25 year old woman.
b) Find the age at which the normal systolic pressure is 125 mm Hg.
4. If an object is thrown upward on Earth from a height of 50 feet, with an initial velocity of 32 feet per second, then its height after t seconds is given by , where h is in feet.
a) After how many seconds will it reach a height of 30 feet?
b) What is the maximum height achieved by the object?
c) How long does it take to reach the maximum height?
d) How long does it take to fall back to the Earth?
5. An astronaut on the moon throws a baseball upward. The height h of the ball, in feet, x seconds after he throws it, is given by the equation.
a) After how many seconds is the ball 12 feet above the moon’s surface?
b) Estimate the acceleration due to gravity on the surface of the moon.
c) What is the initial velocity of the ball?
d) What was the initial height of the ball?
6. An object is propelled upward from a height of 4 ft with an initial velocity of 12 ft/sec.
a) Write an equation to model the height, h, of the object based on the time, t, that it is in the air.
b) What is the maximum height that is achieved by the object?
c) How long does it take for the object to reach the maximum height?
7. In 1940, Emanual Zacchini of Italy was fired a record distance of 175 feet from a cannon while performing in the United States. Suppose his initial velocity was 80 feet per second. His height, h, can be represented by the function, where t represents the number of seconds that have passed. How long after he was shot out of the cannon did he reach his maximum height?
8. In 1942, I.M. Chisov of the USSR bailed out of an airplane without a parachute at 21,980 feet and survived. The function describes the relationship between height, h, in feet and time, t, in seconds. About how many seconds did he fall before reaching the ground?
9. A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula provided that. How many ovens must be manufactured in a given week to generate a profit of $1250?
10. Suppose an object is dropped from a height of 288 ft above the ground.
a) Write an equation to model the height h in terms of the time t in seconds since it was dropped.
b) How long does it take for the object to hit the ground?
11. A ball is thrown straight upward at an initial speed of 40 ft/s.
a) When does the ball reach a height of 24 ft?
b) When does it reach a height of 48 ft?
c) What is the greatest height reached by the ball?
d) When does the ball reach the highest point of its path?
e) When does the ball hit the ground?