Answer:
c. 4.1 s
Step-by-step explanation:
We have been given that a car drives horizontally off a 83-m-high cliff at a speed of 25 m/s . Ignore air resistance.
To solve our given problem, we will use free fall formula. The free fall formula states that the distance the object falls, or height, h, is 1/2 gravity times the square of the time falling.
[tex]h=\frac{1}{2}gt^2[/tex]
Solve for t:
[tex]2*h=2*\frac{1}{2}gt^2[/tex]
[tex]2h=gt^2[/tex]
[tex]\frac{2h}{g}=\frac{gt^2}{g}[/tex]
[tex]\frac{2h}{g}=t^2[/tex]
Switch sides:
[tex]t^2=\frac{2h}{g}[/tex]
Take positive square root:
[tex]t=\sqrt{\frac{2h}{g}}[/tex]
In our given situation [tex]h=83\text{ m}[/tex]. We know [tex]g=9.81\frac{m}{s^2}[/tex].
[tex]t=\sqrt{\frac{2(83m)}{9.81\frac{m}{s^2}}}[/tex]
[tex]t=\sqrt{\frac{166}{9.81}s^2}[/tex]
[tex]t=\sqrt{16.9215086646279307s^2}[/tex]
[tex]t=4.113576140s[/tex]
[tex]t\approx 4.1s[/tex]
Therefore, it will take 4.1 seconds the car to hit the ground and option 'c' is the correct choice.
