Final answer:
The car will hit the ground approximately 104.22 meters away from the base of the cliff after approximately 3.86 seconds.
Step-by-step explanation:
To determine how far the car will hit from the base of the cliff, we can use the equation of motion for an object in freefall. When an object is in freefall, its vertical distance can be calculated using the equation:
H = (1/2) * g * t^2
Where H is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. In this case, since the car is driving horizontally off the cliff, it will hit the ground after the same time it would take for a dropped object to fall from the height of the cliff.
Using the equation H = (1/2) * g * t^2 and the given height of the cliff (73 m), we can solve for t:
73 m = (1/2) * 9.8 m/s^2 * t^2
Simplifying the equation, we find t^2 = (2 * 73 m) / (9.8 m/s^2) = 14.9 s^2. Taking the square root of both sides, we get t = 3.86 s.
Therefore, it will take approximately 3.86 seconds for the car to hit the ground. Since the car is driving horizontally, it will hit the ground approximately 27 m/s * 3.86 s = 104.22 meters away from the base of the cliff.