A police car observes a truck traveling a 110kmph. The police car starts pursuit 30secs after the observation, accelerate to 160kmph in 20secs. Assuming the speeds are maintained const on a straight road, how far from the observation point, will the chase end?
t seconds from the time of observation, the truck has gone
110km/hr * 1hr/3600s * 1000m/km * t s= 30.55t m
cop car has accelerated at
44.44 m/s / 20s = 2.22 m/s^2
so its distance is
1.11 * 20^2 + (44.44(t-30))
so set them equal, and you find that the cop caught up after 64 seconds.
In that time, the truck has gone
160 * 64/3600 = 2.844 km
To find out how far from the observation point the chase will end, we need to calculate the distance traveled by both the truck and the police car during the pursuit.
We can start by finding out how far the truck traveled in the 30 seconds before the police car started the pursuit. The truck's speed is given as 110 km/h, so we can calculate the distance using the formula Distance = Speed x Time. In this case, the time is 30 seconds.
Distance truck = 110 km/h * (30 seconds / 3600 seconds) (we divide by 3600 seconds to convert from seconds to hours)
Distance truck = (110 km/h * 0.00833 h)
Distance truck = 0.92 km
Now we need to calculate the distance traveled by the police car. The police car accelerates to a speed of 160 km/h in 20 seconds. We can again use the formula Distance = Speed x Time.
Distance police car = 160 km/h * (20 seconds / 3600 seconds)
Distance police car = (160 km/h * 0.00556 h)
Distance police car = 0.89 km
Since the chase starts 0.92 km away from the observation point, and the police car travels 0.89 km during the pursuit, we can add these distances together to find the total distance covered by the chase.
Total distance = Distance truck + Distance police car
Total distance = 0.92 km + 0.89 km
Total distance = 1.81 km
Therefore, the chase will end approximately 1.81 km away from the observation point.