A car travelling at a constant speed of 30.0m/s passes a trooper on a motorbike hidden behind a biilboard.2s later a speeding car passes the billboard,the trooper sets off in chase with a constand acceleration of 4.00m/s squared. How long does it take the trooper to pass the speeding car?
Your school subject is "national university of Lesotho"? I've heard of math, physics, and other subjects, but not this one.
To solve this problem, we need to take into account the initial speed of the trooper, the acceleration of the trooper, and the time it takes for the trooper to catch up to the speeding car.
Let's break down the steps to find the time it takes for the trooper to pass the speeding car:
1. Calculate the distance traveled by the car in the 2s interval before the trooper starts.
The car's speed is given as 30.0 m/s, and the time interval is 2s. Using the formula: distance = speed × time, we have:
Distance traveled by the car = 30.0 m/s × 2s
Distance traveled by the car = 60.0 meters
2. Determine the equation of motion for the trooper in terms of time.
The trooper's motion is characterized by constant acceleration. We will use the equation: distance = initial velocity × time + (1/2) × acceleration × time^2.
The initial velocity of the trooper is 0 m/s since they start from rest, and the acceleration is 4.00 m/s^2. Let's denote the time taken by the trooper to catch up to the car as t.
Distance traveled by the trooper = 0 × t + (1/2) × 4.00 m/s^2 × t^2
Distance traveled by the trooper = (1/2) × 4.00 m/s^2 × t^2
Distance traveled by the trooper = 2.00 m/s^2 × t^2
3. Equate the distances traveled by the car and the trooper to find the time.
Since the trooper catches up to the car, the distances traveled by the car and the trooper are equal. We can set up an equation to solve for t:
60.0 meters = 2.0 m/s^2 × t^2
4. Solve for t.
To solve for t, we need to isolate t^2. Divide both sides of the equation by 2.0 m/s^2:
t^2 = 60.0 meters / 2.00 m/s^2
t^2 = 30.0 seconds
Take the square root of both sides to solve for t:
t = √30.0 seconds
t ≈ 5.48 seconds
Therefore, it takes approximately 5.48 seconds for the trooper to pass the speeding car.