Title: A-SSE Throwing a Ball

Alignments to Content Standard: HAS-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

Problem:

A big ball is thrown from a top of a 24m building with an initial velocity of 20 m/s and as the ball is falling, gravity acts on the ball pulling it downward towards the ground. The speed of the ball changes by a rate of 4m/s^2. What is the time in seconds that the ball hits the ground?

Commentary:

The purpose of this task is for students to first build a quadratic equation from the information given, factor the quadratic equation, and solve for the zeros to find the correct time of the ball hitting the ground.

Solution:

The height of the ball starts at 24m.

It travels at an initial velocity of 20 m/s.

Gravity pulls the ball downward towards the ground, changing the speed by 4m/s^2.

t is for time.

 

 

 

The quadratic equation is -4t^2 +20t +24

 

This can be factored into (4t + 4) (-t +6) = 0

Set both binomials equal to 0 and solve for t.

4t +4 =0                -t +6 =0

4t = -4                     t = 6

t = -1

Because you cannot have a negative time, the ball hits the ground after 6 seconds.