A police car moveing at 140 km/h is changing a lorry moveing at 120 km/h.If the initial distance betwen them is 500m,how many minutes later and at what distance from its initial position does the police carb catch the lorry
The distance between them decreases ar 20 km/h rate. What is 0.5 km/20 km/h?
0.025 h = 1.5 minutes.
To determine when and where the police car catches up to the lorry, we need to calculate the time it takes for the police car to close the initial distance between them and find the distance covered by both vehicles in that time.
First, let's convert their speeds to meters per second (m/s) for consistent units:
Speed of the police car = 140 km/h = (140 * 1000) / (60 * 60) m/s ≈ 38.89 m/s
Speed of the lorry = 120 km/h = (120 * 1000) / (60 * 60) m/s ≈ 33.33 m/s
Next, let's find the time taken for the police car to close the initial distance:
Distance = Initial distance between them = 500 m
Relative speed = Speed of the police car - Speed of the lorry = 38.89 m/s - 33.33 m/s = 5.56 m/s
Time = Distance / Relative speed = 500 m / 5.56 m/s ≈ 89.83 seconds
Now, let's convert the time into minutes:
Time in minutes = 89.83 seconds / 60 seconds/minute ≈ 1.5 minutes
Therefore, the police car catches the lorry approximately 1.5 minutes later.
To find the distance from the police car's initial position, we need to calculate the distance covered by the police car in that time:
Distance covered by the police car = Speed of the police car * Time
Distance covered by the police car = 38.89 m/s * 89.83 seconds ≈ 3490.96 meters
Distance from the police car's initial position = Initial distance + Distance covered by the police car
Distance from the police car's initial position = 500 m + 3490.96 m ≈ 3990.96 meters
Therefore, the police car catches the lorry approximately 1.5 minutes later at a distance of approximately 3990.96 meters from its initial position.