Math Is Fun Forum

jadewest

Member

Registered: 2021-02-20

Posts: 44

Quadratic equations

Hello,
I need help with this exercise.

A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform.  The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60.   How long before the ball hits the ground?

Best,
Jade

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Quadratic equations

Heya Jade,
I'm going to answer this thread(and not the other one, as the details appear to be the same.)
To determine when the ball hits the ground, solve the equation when h equals 0.
You can either complete the sqiare or use the quadratic formula. For the sake of simplicity, I'm going to proceed using the latter method, but either one is fine.

For a quadratic equation

the roots are

So plug in the relevant coefficients, and solve as follows:

You get

. The negative solution obviously doesn't make sense, so strike it out, and you're left with the actual answer, 6.092 seconds.
Here's a useful graph visualizing the vertical elevation of the ball through its flight with the two roots of the equation.

Last edited by Mathegocart (2022-07-04 09:11:09)

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