A police jeep is chasing a culpritgoing on a motorbike. The motorbike crosses a turning at a sped of72km/hr.the jeep follows it a speed of 90km/hr, crossing the turning ten seconds later than bike , assuming that they travel at a constant speed , how far from the turnin will the jeep catch up with a bike

To solve the problem of how far from the turning the police jeep will catch up with the motorbike, we need to analyze the speeds of both vehicles and the time difference in their departures. Let's break it down step by step.

Understanding the Scenario

The motorbike is traveling at a speed of 72 km/hr, while the police jeep is moving faster at 90 km/hr. The crucial detail here is that the jeep starts its chase 10 seconds after the motorbike has already begun moving. This time difference is essential for calculating how far the motorbike has traveled before the jeep starts its pursuit.

Converting Speeds to Consistent Units

First, we need to convert the speeds from kilometers per hour to meters per second, as this will help us work with the time difference more easily. The conversion factor is:

• 1 km/hr = 1/3.6 m/s

So, we convert the speeds:

• Motorbike: 72 km/hr = 72 / 3.6 = 20 m/s
• Jeep: 90 km/hr = 90 / 3.6 = 25 m/s

Calculating the Head Start of the Motorbike

Next, we need to determine how far the motorbike travels during the 10 seconds before the jeep starts chasing. We can use the formula:

Distance = Speed × Time

For the motorbike:

• Distance = 20 m/s × 10 s = 200 meters

This means that when the jeep starts its pursuit, the motorbike is already 200 meters ahead.

Determining the Catch-Up Time

Now, we need to find out how long it will take for the jeep to catch up to the motorbike. The jeep is closing the gap at a rate equal to the difference in their speeds:

• Relative Speed = Speed of Jeep - Speed of Motorbike = 25 m/s - 20 m/s = 5 m/s

To find the time it takes for the jeep to cover the 200 meters gap, we can use the formula:

Time = Distance / Speed

Thus, the time taken for the jeep to catch up is:

• Time = 200 meters / 5 m/s = 40 seconds

Calculating the Distance from the Turning Point

Finally, we can find out how far from the turning point the jeep catches up with the motorbike. During the 40 seconds it takes for the jeep to catch up, both vehicles are still moving. We can calculate the distance traveled by the motorbike during this time:

Distance traveled by the motorbike in 40 seconds:

• Distance = Speed × Time = 20 m/s × 40 s = 800 meters

Now, we add the initial 200 meters head start to this distance:

• Total Distance from the turning = 200 meters + 800 meters = 1000 meters

In summary, the police jeep will catch up with the motorbike 1000 meters from the turning point. This problem illustrates how relative speeds and time differences can be used to solve real-world scenarios involving motion.