A skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. the function h = −16t^2 28t 8 represents the height h (in feet) of the skier after t seconds. the skier has a perfect landing. how many points does the skier earn? 1 point per foot in the air, 5 points per second in the air, and a perfect landing is 25 points.
Accepted Solution
A:
The skier earns 35.875 points.
We can find the height in the air by using -b/2a: -28/2(-16) = -28/-32 = 0.875
This will give the skier 0.875 points.
To find the amount of time in the air, we solve the related equation: 0=-16t²+28t+8
We will first factor out the GCF, -4: 0=-4(4t²-7t-2)
Now we will factor the trinomial in parentheses using grouping. We want factors of 4(-2)=-8 that sum to -7; -8(1) = -8 and -8+1=-7. This is how we will "split up" bx: 0=-4(4t²-8t+1t-2)
Now we will group the first two and last two terms: 0=-4[(4t²-8t)+(1t-2)]
We will factor out the GCF of each group: 0=-4[4t(t-2)+1(t-2)]
This gives us the factored form: 0=-4(4t+1)(t-2)
Using the zero product property, we know that either t-2=0 or 4t+1=0: t-2=0 t-2+2=0+2 t=2
4t+1=0 4t+1-1=0-1 4t=-1 4t/4 = -1/4 t=-1/4
Negative time makes no sense, so t=2. This gives the skier 5(2) = 10 points.
Counting the perfect landing, we have 25+10+0.875 = 35.875 points.