A 97 dodge neon locks it's brakes up and skids 15 ft before hitting a motorcyclist then continues to skid another 130 ft without throwing the rider or motorcycle out from in front of the car. The only damage to car is busted head light and bumper comes off the motorcyclist only has a broken wrist
How fast was the car going when it hit the motorcycle
To determine the speed of the car when it hit the motorcycle, we can use the principles of physics and the information provided.
First, we need to calculate the coefficient of friction between the car's tires and the road surface, which is needed to estimate the deceleration of the car. The coefficient of friction can vary depending on various factors like the condition of the road, tire quality, and brake conditions.
Let's assume a coefficient of friction of μ for the car's tires. The deceleration of the car can be calculated using the formula:
Deceleration (a) = g * μ
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the car skidded 15 ft before hitting the motorcyclist, we need to convert this distance into meters. Since 1 foot is approximately 0.3048 meters, the skidding distance can be calculated as:
Skidding distance before hitting the motorcyclist = 15 ft * 0.3048 m/ft
Next, we need to determine the time it took for the car to cover this distance. The formula for distance covered during constant acceleration can be used:
Distance (d) = (Initial Velocity (u) * t) + (0.5 * a * t^2)
Since the initial velocity is zero, the equation simplifies to:
Distance (d) = 0.5 * a * t^2
Solving for time (t), we get:
t = √(2 * d / a)
Now that we have the time taken to cover the skidding distance before hitting the motorcyclist, we can calculate the car's initial velocity (u) using the formula:
Initial Velocity (u) = a * t
Finally, we need to determine the car's speed when it hit the motorcycle. To do this, we can use the conservation of linear momentum. The momentum before the collision is equal to the momentum after the collision:
Initial Momentum = Final Momentum
The initial momentum is the product of the car's mass (m) and its initial velocity (u). Assuming the mass of the car is known, the initial momentum can be calculated.
The final momentum is the sum of the car's mass (m) multiplied by its final velocity (v) and the motorcyclist's mass (M) multiplied by the motorcyclist's velocity (V). Since the motorcyclist is not thrown from in front of the car, we can assume their speed remains constant.
Therefore, the equation is:
m * u = m * v + M * V
Rearranging the equation, we can solve for the final velocity (v):
v = (m * u - M * V) / m
Given the skidding distance after hitting the motorcyclist (130 ft), we can apply the same calculations as before to convert it into meters.
By following these steps and using the appropriate values, you can calculate the car's speed when it hit the motorcycle. Please note that this calculation relies on several assumptions, such as constant coefficients of friction and constant velocities of the motorcyclist. Actual road conditions and other factors may affect the accuracy of the result.