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.