Problema Solution
A snowboarder leaves an 8-foot-tall ramp with an upward velocity of 28 feet per second. The function h=-16t^2+28t+8 gives the height h (in feet) of the snowboarder after t seconds. The snowboarder earns 1 point per foot of the maximum height reached, 5 points per second in the air, and 25 points for a perfect landing. With a perfect landing, how many total points does the snowboarder receive?
Answer provided by our tutors
First we will find the maximum height.
We need to find the maximum of the parabolic function h=-16t^2+28t+8
h max = c - b^2/4a, where a = -16, b = 28, c = 8
h max = 8^2 - 28^2/(4*(-16))
h max = 76.25 ft
Thus the points from the maximum height reached are 76 points.
Next we find the maximum time in air by solving the equation h = 0 that is
-16t^2+28t+8 = 0
........
........
t = 2 s
The points from seconds in the air are: 2*5 = 10 points
The total number of points is: 76 + 10 + 25 = 111 points.