Final answer:
To determine the speed of the car as it drove off a cliff, we calculated the time of free fall using the vertical distance and then found the horizontal velocity by dividing the horizontal distance traveled by the time of fall, resulting in a speed of 23.4 m/s.
Step-by-step explanation:
The student's question involves calculating the initial speed of a car as it drives off a cliff, using principles of projectile motion from Physics. To solve this, we can apply kinematic equations for the horizontal and vertical motion separately. The car's horizontal velocity remains constant since no acceleration occurs in the horizontal direction (ignoring air resistance). On the other hand, the vertical motion is influenced by gravity.
We are given a cliff height (50 m), which represents the vertical displacement (y), and the distance from the base of the cliff where the car landed (75 m), which represents the horizontal displacement (x). To find the time it takes for the car to fall, we use the equation for vertical displacement under free fall, assuming gravity (g) to be 9.8 m/s2:
y = (1/2)gt2
Solving for t (time), we get:
t = sqrt((2y)/g) = sqrt((2*50 m)/(9.8 m/s2)) = sqrt(10.2 s2) = 3.2 s
Now that we have the time, we can find the horizontal velocity (vx) using the horizontal displacement:
x = vx*t
So:
vx = x/t = 75 m / 3.2 s = 23.4 m/s
Thus, the car was traveling at 23.4 m/s when it left the edge of the cliff.