Suppose that you are an accident investigator and you are asked to figure whether or not the car was speeding before it crashed through the rail of the bridge and into the mudbank. The speed limit on the bridge is 55 mph = 24 m/s. What is your conclusion?( The vertical component is 4.9m/s and the horizontal component is 24 m.)PROJECTILE CONCEPT!!!!!!!!!!
To determine whether or not the car was speeding before the crash, we can analyze the projectile motion of the car as it went through the rail of the bridge and into the mudbank.
Projectile motion consists of two components: the vertical component and the horizontal component.
Given:
Horizontal component (initial velocity in the x-direction) = 24 m/s
Vertical component (initial velocity in the y-direction) = 4.9 m/s
To analyze the motion, let's split the components of the motion:
1. Vertical Component:
The vertical component of the motion is influenced by gravity. Since the vertical velocity is 4.9 m/s, this means the car had an upward velocity component at some point.
2. Horizontal Component:
The horizontal component only experiences a constant velocity, assuming there is no horizontal force acting upon it.
To determine the speed of the car, we can calculate its magnitude (or resultant) velocity. We can use the Pythagorean theorem:
Resultant velocity (v) = √(horizontal velocity^2 + vertical velocity^2)
Plugging in the given values:
v = √(24 m/s^2 + 4.9 m/s^2)
v = √(576 + 24.01)
v = √600.01
v ≈ 24.49 m/s
The magnitude of the resultant velocity of the car is approximately 24.49 m/s.
To determine whether the car was speeding or not, we need to compare the resultant velocity to the speed limit of 24 m/s:
Since the magnitude of the resultant velocity (24.49 m/s) is greater than the speed limit (24 m/s), this indicates that the car was speeding before it crashed through the rail of the bridge and into the mudbank.
Conclusion: The car was speeding before the crash.
To determine whether the car was speeding, we need to analyze the motion of the car using the projectile concept. In this case, we have two components of the car's motion: the vertical component and the horizontal component.
Given:
Vertical component (v_y) = 4.9 m/s (upward direction)
Horizontal component (v_x) = 24 m/s (forward direction)
To find out if the car was speeding, we need to determine the car's resultant velocity and compare it to the speed limit.
The resultant velocity (v) of the car can be found using the Pythagorean theorem:
v = √(v_x^2 + v_y^2)
v = √((24)^2 + (4.9)^2)
v ≈ 24.6 m/s
Comparing the resultant velocity (24.6 m/s) to the speed limit (24 m/s), we can conclude that the car was indeed speeding before it crashed through the rail of the bridge.
Remember, to analyze the motion, we used the equations of motion and the Pythagorean theorem to find the resultant velocity.