During a car race two cars,a ferarri and a mercedes crashed.The ferarri was travelling at a speed of 340km/h an the mercedes was travelling at a speed of 230km/h.What is the resultant crash
To determine the result of the crash, we need to consider the velocities of the two cars. The resultant crash can be understood by computing the vector sum of the velocities of the two cars at the time of collision.
To find the resultant velocity, we can use vector addition.
Step 1: Convert the velocities to a common unit - let's use meters per second (m/s) for consistency.
The velocity of the Ferrari is given as 340 km/h. To convert this to m/s, we need to multiply it by 1000 (to convert to meters) and divide by 3600 (to convert to seconds):
340 km/h = (340 * 1000) / 3600 m/s ≈ 94.44 m/s (rounded to two decimal places)
The velocity of the Mercedes is given as 230 km/h. Similarly, converting to m/s:
230 km/h = (230 * 1000) / 3600 m/s ≈ 63.89 m/s (rounded to two decimal places)
Step 2: Perform vector addition to find the resultant velocity.
To add the velocities together, we need to consider both magnitude and direction. We can form a right-angled triangle using the velocities of the two cars as the triangle's sides. The resultant velocity will be the hypotenuse of this triangle.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity:
Resultant velocity = √(94.44^2 + 63.89^2) ≈ 113.35 m/s (rounded to two decimal places)
Step 3: Determine the direction of the resultant velocity.
To determine the direction, we can use trigonometry. We can find the angle between the resultant velocity and one of the initial velocities by using the inverse tangent function:
Angle = arctan(63.89 / 94.44)
Using a calculator, we can find that the angle is approximately 34.85 degrees (rounded to two decimal places).
Therefore, based on the given information, the resultant crash has a magnitude of approximately 113.35 m/s and a direction of approximately 34.85 degrees relative to the initial velocity of the Ferrari.