Answer:
The time it takes the ball to land on green is 4.4175 seconds
Step-by-step explanation:
Given
Equation for number of seconds it take to hit the green: −16t² + 70t + 6 = −3
Required
The value of t.
The interpretation of this question is that, we should solve for t in the above equation.
-16t² + 70t + 6 = −3
Collect like terms
-16t² + 70t + 6 - 3 = 0
-16t² + 70t + 3 = 0
Multiply through by -1
-1(-16t² + 70t + 3) = -1 * 0
16t² - 70t - 3 = 0
Solving using quadratic formula.
[tex]t = \frac{-b+-\sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 16, b = -70, c = -3
t = (-(-70) ± √(-70² - 4 * 16 * -3))/(2 * 16)
[tex]t = \frac{-(-70)+-\sqrt{(-70)^2 - 4 * 16 * -3}}{2 * 16}[/tex]
t = (70 ± √(4900 + 192))/32
[tex]t = \frac{70+-\sqrt{4900 + 192}}{32}[/tex]
[tex]t = \frac{70+-\sqrt{5092}}{32}[/tex]
[tex]t = \frac{70+-71.36}{32}[/tex]
[tex]t = \frac{70+71.36}{32}[/tex] or [tex]t = \frac{70-71.36}{32}[/tex]
[tex]t = \frac{141.36}{32}[/tex] or [tex]t = \frac{-1.36}{32}[/tex]
[tex]t = 4.4175 \\ or\\ t =-0.0425[/tex]
But t can't be negative.
So, t = 4.4175
The time it takes the ball to land on green is 4.4175 seconds
