Answer:
A) 3.39 seconds
Explanation:
A) How long will it take the arrow to hit the ground?
We can find the time it takes the arrow to hit the ground by using a constant acceleration equation.
Let's make the positive direction upwards and the negative direction downwards. Let's list out the relevant variables:
- v₀ = -60 m/s
- Δy = -200 m
- a = -9.8 m/s²
- t = ?
Find a constant acceleration equation that contains these four variables.
Substitute known values into the formula and solve for t.
- -200 = (-60 · cos(45))t + 1/2(-9.8)t²
- -200 = (-30√2)t - 4.9t²
- 0 = -4.9t² - (30√2)t + 200
Use the quadratic formula to continue solving for t.
- [tex]\displaystyle \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
- [tex]\displaystyle \frac{-(-30\sqrt{2})\pm \sqrt{(-30\sqrt{2})^2 -4(-4.9)(200)} }{2(-4.9)}[/tex]
- [tex]\displaystyle \frac{30\sqrt{2} \pm \sqrt{1800+3920} }{-9.8}[/tex]
- [tex]\displaystyle \frac{30\sqrt{2} \pm \sqrt{5720} }{-9.8}[/tex]
From this, when we add the discriminant we get -12.04664168. When we subtract the discriminant we get 3.38819129.
Since time cannot be negative, the time it takes for the arrow to hit the ground must be 3.39 seconds.
