Final answer:
The time it takes for a car to hit the ground after driving off a 75 meter high cliff at a horizontal speed of 31 m/s can be calculated using kinematic equations. The correct calculation shows that it will take approximately 3.9 seconds for the car to hit the ground, making option a the correct answer.
Step-by-step explanation:
The student's question involves calculating the time it takes for a car to hit the ground after driving horizontally off a cliff, which is a physics problem involving kinematics. To solve this, we use the equation for the time of flight in free fall, which is derived from the formula for the distance traveled under constant acceleration (gravity in this case):
d = ½ * g * t^2
Here, d is the vertical distance to the ground (75 m), g is the acceleration due to gravity (approximately 9.81 m/s^2), and t is the time in seconds. Plugging in the numbers and solving for t, the formula becomes:
75 m = ½ * 9.81 m/s^2 * t^2
By rearranging and solving the equation for time, we find that t = √(2 * d / g), or:
t = √(2 * 75 m / 9.81 m/s^2)
t ≈ √(15.27)
t ≈ 3.9 s
The correct answer is 3.9 seconds (option a), and this is the duration it will take for the car to hit the ground after driving off a 75 meter high cliff at a constant horizontal speed of 31 m/s, ignoring air resistance.