Question 50986: I need the method for solving this more than the answer, but both would be appreciated:
Mark launched a model rocket using an engine which will generate a speed of 180 feet per second. The formula h = rt - 16t squared gives the height of an object projected upward at a rate of r feet per second after t seconds. After how many seconds will Mark's rocket reach a height of 464 feet? After how many seconds will it be at that height again? Thank you.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Step 1.
Rewrite your equation in the form of a quadratic function.
 This is function for the height, h, of an object propelled upwards as a function of time, t. Here, r is given as 180 ft/sec. This fits the situation of Mark's rocket. You are being asked to find at what time, t, will the height, h, be 464 feet. Because your equation is quadratic, you can expect to get two solutions.
Step 2. Set h(t) = 464 in the quadratic equation above and solve for t.
 Put this into standard form by subtracting 464 from both sides.
Step 3. Solve the quadratic equation for t by the most convenient method. You can simplify this equation a bit by dividing through by -4 to get:
 Now you can factor this.
 Apply the zero product principle:
 and/or 
If then t = 4
If then  or 
The two solution are:
The height of the rocket will reach 464 feet in 4 seconds, ascending.
The height of the rocket will be at 464 feet again in 7.25 seconds descending.
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