Question

I do not understand how to solve these kinds of questions at all :/. A juggler is performing an act by juggling several balls. The juggler throws the balls up at an initial height of 3.9 feet with a speed of 14.8 feet per second. If the juggler did not catch a ball, about how long will it take the ball to hit the floor?

Answer 1

Sure I can help you with this, but what kind of class is this for and what other background knowledge do you know?

Answer 2

This is for Algebra I. Has to do with solving quadratic equations using real-world examples.

Answer 3

Okay.... so\[y = ax^2 + bx + c\]
is your general form of the quadratic equation. I'm not sure if they have given you this information but it's essential to getting a solution. In this case the variable a is the Earth's acceleration due to gravity, use 32. For b use your intial speed (14.8) and for c use your intial height 3.9, then in this case use x to represent time, if you set y=0 this means the final value of the height is 0 (The ground)

Answer 4

So in other words 32x^2 + 14.8x + 3.9 = 0. And with other eqauations how will I know which of the variables are a,b, and c?

Answer 5

Think about what the units of the equaation are. In this case you know that y represents height, so that's measured in feet. So every other component must be in feet to be added. The c was already in feet, that was your inital height. That's your intial condition, think of it like...even if x=0, it would already be at that height. Then for b, so for the term bx to be in terms of feet, you need a unit that take time and make it into feet so b was a speed, feet/sec so when multiplied by time, they canceled out. And because for the ax^2 term the x is squared you would need feet/second^2 in this case that unit represents acceleration

Answer 6

Thanks so much!

Answer 7

Sorry for that explanation...it's not the best. Once you get a lot further in math...like calculus quadratic equations make A LOT of sense, and this example is based in Physics so I tried my best!