Answer:
The car will take approximately 4.865 seconds to splash into the water.
Explanation:
Let suppose that car moves initially downwards. We must see the kinematics of the car after being thrown off the bridge, it is quite certain that car experiment a free fall, in which it is accelerated uniformly by gravity. The time spent by the car to splash into the water is obtained from this equation of motion:
[tex]y = y_{o}+v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex]
Where:
[tex]y[/tex] - Current height, measured in feet.
[tex]y_{o}[/tex] - Initial height, measured in feet.
[tex]v_{o}[/tex] - Initial velocity, measured in feet per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
If we know that [tex]y = 0\,ft[/tex], [tex]y_{o} = 624\,ft[/tex], [tex]v_{o} = -50\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], this quadratic function is obtained:
[tex]-16.087\cdot t^{2}-50\cdot t +624 = 0[/tex]
Now we get the roots of the polynomial by Quadratic Formula:
[tex]t_{1} \approx 4.865\,s[/tex], [tex]t_{2} \approx -7.973\,s[/tex]
Only the first root is physically reasonable. In a nutshell, the car will take approximately 4.865 seconds to splash into the water.
