A car drives straight off the edge of a cliff that is 56 m high. The police at the scene of the accident note that the point of impact is 129 m from the base of the cliff. How fast was the car traveling when it went over the cliff?
how long does it take the car to fall 56m?
what velocity does it take to go 129m/that time?
1. 5.714 seconds
2. 50.5mph, 81.27kph, or 22.576mps
1. 5.714 seconds
2. 50.5mph, 81.27kph, or 22.576mps (meters per second)
Wait disregard that - I am such an idiot right now. (I can't erase the former comments)
1. 3.379 seconds
2. 85.549mph, 137.678kmph, or 38.244mps (meters per second)
I was a little braindead before and miscalculated the projection formula by not doubling the gravitational free fall factor with each passing second.
NOTE: this does not count the concepts of mass vs wind resistance - just a simple projection calculation.
To determine the speed of the car when it went over the cliff, we can use the principles of projectile motion. The key variables we need are the height of the cliff (h) and the horizontal distance traveled (d) before hitting the ground.
Given:
Height of the cliff (h) = 56 m
Horizontal distance traveled (d) = 129 m
We can use the formula for the vertical motion of a projectile to calculate the initial vertical velocity (Vy) of the car:
Vy^2 = Vo^2 + 2gh
Where:
Vy is the final vertical velocity (0 m/s as it hits the ground)
Vo is the initial vertical velocity
g is the acceleration due to gravity (-9.8 m/s^2)
h is the height of the cliff (56 m)
Rearranging the equation, we get:
Vo = sqrt(Vy^2 - 2gh)
Since the final vertical velocity (Vy) is 0 m/s when it hits the ground, we can simplify the equation to:
Vo = sqrt(2gh)
Now, we need to calculate the initial vertical velocity (Vo). Substituting the given values:
Vo = sqrt(2 * 9.8 * 56)
= sqrt(1097.6)
= 33.1 m/s (approximately)
The initial velocity (V) of the car can be obtained by using the formula for horizontal motion:
V = d / t
Where:
V is the initial velocity
d is the horizontal distance traveled (129 m)
t is the time of flight
Since the car starts from rest vertically and is only affected by gravity, the time of flight can be found using:
h = 0.5 * g * t^2
Substituting the given values:
56 = 0.5 * 9.8 * t^2
Simplifying the equation:
t^2 = 56 / (0.5 * 9.8)
t^2 = 11.4
t ≈ 3.38 s (approximately)
Now, we can find the initial velocity (V) using the formula:
V = d / t
V = 129 / 3.38
V ≈ 38.2 m/s (approximately)
Therefore, the car was traveling at approximately 38.2 m/s when it went over the cliff.