A car drives straight off the edge of a cliff that is 60 m high. The police at the scene of the accident observed that the point of impact is 126 m from the base of the cliff. How fast was the car traveling when it went over the cliff?
it traveled 126m in √(2*60/9.8) seconds.
so, v = 36.0 m/s = 129.6 km/hr
7yu
To determine the speed of the car when it went over the cliff, we can use the principles of projectile motion. The key formula to use in this case is the range equation:
range = (initial velocity) * (time of flight)
In this scenario, the car is launched horizontally off the cliff, which means its initial vertical velocity is zero. Therefore, we can ignore the vertical component of motion.
We need to find the time of flight, which is the time it takes for the car to travel horizontally from the cliff to the point of impact. Since the only horizontal force acting on the car is its initial velocity, the time of flight can be found using the formula:
range = (initial velocity) * (time of flight)
Substituting the given values, we have:
126 m = (initial velocity) * (time of flight)
Now, let's find the time of flight:
time of flight = 126 m / (initial velocity)
Next, we need to determine the vertical distance the car traveled before hitting the ground. The car experiences free fall motion as it falls vertically from the cliff, so we can use the kinematic equation:
h = (1/2) * g * t^2
In this equation, h represents the vertical distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time of flight.
Substituting the given values, we have:
60 m = (1/2) * 9.8 m/s^2 * (time of flight)^2
Rearranging the equation, we can solve for the time of flight:
(time of flight)^2 = (2 * 60 m) / 9.8 m/s^2
Finally, we can calculate the time of flight:
time of flight = sqrt((2 * 60 m) / 9.8 m/s^2)
Now that we have the value for the time of flight, we can substitute it back into the equation for the horizontal range to find the initial velocity:
126 m = (initial velocity) * (time of flight)
Solving for the initial velocity:
(initial velocity) = 126 m / (time of flight)
Calculating this value will give us the speed at which the car was traveling when it went over the cliff.