QUADRATIC EQUATION WORD PROBLEMS
1a.) What is the equation relating the height of an object to the time after its launch? (Thrown Object Model)
1b.) What is the equation that gives the time at maximum height?
1c.) Complete the sentence: If you throw an object downwards, then v is (positive, negative)
2a.) An object is launched straight up at 20 feet per second from off the side of the top of a 60-foot tall platform. When does the object strike the ground?
2b.) When did the object in question #3 attain maximum height? ______after launch
What was the maximum height? ______
3.) Ashley throws a penny off a 1,000 foot tall tower with an initial downward velocity of 6 feet per second. How long until it hits the ground?
4a.) Resolve problem #3 if she threw the penny upwards at 6 feet per second instead.
4b.) When did the penny that was thrown upwards reach its maximum height? ______after launch
What was the maximum height? ______
5.) A closed box with a square base must measure exactly 24 inches high and have a surface area of 500 square inches. What must be the measure of its length?
6.) A pilot clumsily lets a cup of soda fall out of his biplane. If the plane is flying at 3,000 feet, and the cup falls with an initial velocity of 4 feet per second, how long will it take for the cup to hit the ground?
7a.) A bullet is fired from a starter’s pistol straight up into the air at an initial velocity of 450 ft/sec. If the pistol was held at a height of 6 feet when it was fired, how long will it take the bullet to return to the ground?
7b.) When will the bullet reach its maximum height? ______after launch
What was the maximum height? ______
8a.) Darryl throws a ball upwards over a 1200-foot-tall cliff. If he throws it upwards with an initial velocity of 35 feet per second, how long until it hits the ground?
8b.) When will the ball reach its maximum height? ______after launch
What was the maximum height? ______
9.) You need to design a grain tower with a square base that has a height of 150 feet and a surface area no larger than 11,500 square feet, including the floor. What is the maximum length of the base?
Extensions
10.) Brandon throws a ball upwards from a starting height of 4 feet. It lands 3 seconds later. What was the initial velocity?
11a.) Alyssa throws a ball upwards from a starting height of 5 feet. She notices it reaches its highest point 1.7 seconds later. What was the initial velocity?
11b.) What is the highest point the ball reaches?
11c.) When does the ball hit the ground?
12.) A closed box has a base with a length that is twice its width, a height of 30 inches and a surface area of 1,000 square inches. Find:
Length: ______Width: ______Area of the base: ______