A biker traveling with a velocity of 80 feet per second leaves a 100 feet platform and is projected directly upward. The function for the projectile motion
Is s(t) = -16t2 +80t + 100 where s(t) is the height and t is the seconds the biker is in the air.
a. a) Draw a rectangular coordinate system and sketch the height of the biker after the bike leaves the platform. Make the horizontal axis the time the biker is in the air. Label the horizontal and vertical axes. Don't forget that the biker leaves the platform at 100 feet.
b)Use your graphing utility to graph the parabola.
c)Using your graphing calculator, find how many seconds it takes for the biker to reach its maximum height. Compare this value to -b/2a, where a and b are the coefficients found from comparing the form
f(x) = ax2 + bx + c to the given quadratic function. This value, -b/2a, is the x-value of the vertex. Find the y-value at this point by evaluating the function at the x-value of -b/2a. What does the y-value represent at this specific x-value? Then state the (x, y) point of the vertex or maximum point.
d)Looking at your calculator, find the number of seconds the biker is in the air (or "hang time"). Then find the range of height values that the biker attains.
e)State the domain and range of this real life example. Remember that time isn't negative and that the model is valid only when the biker is in the air!
f)Use the graph to determine when the biker will reach a height of 100 feet. State the (these) point(s) as an order pair and using functional notation.
g)Use the graph to determine what height the biker will attain after 1 second. State the point as an ordered pair and using functional notation.
h)Where is the function increasing? In other words, for what x-values does the biker continue to get higher? Where is the function decreasing? In other words, for what x-values does the biker start descending toward the ground? State these intervals using interval notation.