Answer:
The time it will take the mega-ray blaster to hit the ground is 2.57 s.
Explanation:
Given;
initial velocity of Optimus Prime, u = 24 m/s
height of fall of the mega-ray blaster, h = 94 m
The time of fall of the mega-ray blaster is calculated using the following kinematic equation;
[tex]h = ut + \frac{1}{2}gt^2\\\\94 = 24t + \frac{1}{2}(9.8)t^2\\\\94 = 24t + 4.9t^2\\\\4.9t^2 +24t -94 = 0\\\\Use \ formula \ method \ to \ solve \ for \ "t"\\\\a = 4.9 , b = 24, c = -94\\\\t = \frac{-b \ +/- \ \sqrt{b^2 -4ac} }{2a} \\\\t = \frac{-24 \ +/- \ \sqrt{(24)^2 -4(-94 \times4.9)} }{2(4.9)} \\\\t = \frac{-24 \ +/- \ \sqrt{2418.4} }{9.8}\\\\t = \frac{-24 \ +/- \ 49.177 }{9.8}\\\\t = \frac{-24 \ +\ 49.177 }{9.8} \ \ or \ \ t = \frac{-24 \ -\ 49.177 }{9.8} \\\\[/tex]
[tex]t = 2.57 \ s \ \ or \ \ t = -7.47 \ s[/tex]
t = 2.57 s
Therefore, the time it will take the mega-ray blaster to hit the ground is 2.57 s.
