In this discussion you will explore an application of polynomials by studying a model of a free falling object.
Scenario – A person stands at the top of a 30
feet building and throws a ball upwards with an initial velocity of 38
feet per second . Using calculus and the fact that the acceleration due
to gravity is approximately we obtain that the velocity and height of the ball satisfy the following formulas:
Velocity of the ball t seconds after being thrown:
Height of the ball t seconds after being thrown :
Here, velocity v is given in ft/s and the height h is given in ft . The variable t represents time, given in seconds.
Instructions:
Review the scenario above and answer the following questions:
Find the maximum height of the ball (in feet).
Hint: the moment the ball reaches maximum height, its
velocity is zero (because in that split of a millisecond, the ball must
stop to change direction and comeback down)
Determine how long it takes for the ball to hit the ground (in seconds).
Hint: when the ball hits the ground, what is its height equal to? (answer: height is zero)