A car drives horizontally off the edge of a cliff that is 31.4 m high. The police at the scene of the accident note that the point of impact is 114 m from the base of the cliff. How fast was the car traveling when it drove off the cliff?
how long does it take to fall 31.4 m?
speed = distance/time
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Jasma/Jay/..
Be sure to choose ONE name and keep it. Name games are just silly.
To find the speed of the car when it drove off the cliff, we can use the principles of projectile motion.
First, let's denote the initial speed of the car as "v." We need to determine the value of v.
The horizontal distance traveled by the car before hitting the ground is given as 114 m. Since there is no horizontal acceleration, the time of flight can be calculated using the equation:
distance = velocity * time
114 m = v * t
Next, we need to find the time it takes for the car to reach the ground. We can use the vertical distance traveled by the car, which is the height of the cliff, 31.4 m.
The vertical motion of the car can be described using the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
Here, the initial velocity is 0 m/s because the car starts from rest vertically.
31.4 m = 0 * t + (1/2) * 9.8 m/s^2 * t^2
Simplifying the equation:
4.9 * t^2 = 31.4
t^2 = 31.4 / 4.9
t^2 = 6.408163265
Taking the square root of both sides:
t = √6.408163265
t ≈ 2.530 s
Now that we have the time of flight, we can substitute this value back into the equation for horizontal distance:
114 m = v * 2.530 s
Solving for v:
v = 114 m / 2.530 s
v ≈ 45.03 m/s
Therefore, the car was traveling at approximately 45.03 m/s when it drove off the cliff.