Answer:
[tex]t = 1.82[/tex]
Explanation:
Given
[tex]u = 7.70m/s[/tex] -- initial velocity
[tex]s = 30.2m[/tex] --- height
Required
Determine the time to hit the ground
This will be solved using the following motion equation.
[tex]s = ut + \frac{1}{2}gt^2[/tex]
Where
[tex]g = 9,8m/s^2[/tex]
So, we have:
[tex]30.2 = 7.70t + \frac{1}{2} * 9.8 * t^2[/tex]
[tex]30.2 = 7.70t + 4.9 * t^2[/tex]
Subtract 30.2 from both sides
[tex]30.2 -30.2 = 7.70t + 4.9 * t^2 - 30.2[/tex]
[tex]0 = 7.70t + 4.9 * t^2 - 30.2[/tex]
[tex]0 = 7.70t + 4.9t^2 - 30.2[/tex]
[tex]7.70t + 4.9t^2 - 30.2 = 0[/tex]
[tex]4.9t^2 + 7.70t - 30.2 = 0[/tex]
Solve using quadratic formula:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 4.9;\ b = 7.70;\ c = -30.2[/tex]
[tex]t = \frac{-7.70\±\sqrt{7.70^2 - 4*4.9*-30.2}}{2*4.9}[/tex]
[tex]t = \frac{-7.70\±\sqrt{651.21}}{9.8}[/tex]
[tex]t = \frac{-7.70\±25.52}{9.8}[/tex]
Split the expression
[tex]t = \frac{-7.70+25.52}{9.8}[/tex] or [tex]t = \frac{-7.70-25.52}{9.8}[/tex]
[tex]t = \frac{17.82}{9.8}[/tex] or [tex]t = -\frac{33.22}{9.8}[/tex]
Time can't be negative; So, we have:
[tex]t = \frac{17.82}{9.8}[/tex]
[tex]t = 1.82[/tex]
Hence, the time to hit the ground is 1.82 seconds
