5. A boat capable of making 9.0 km/hr in still water is travelling upstream in a river
flowing at 4 km/h. An object lost overboard is not missed for 30 minutes.
(a) If the boat is then turned around, how long will it take to overtake the
floating lost object?
(b) What total distance will the boat travel relative to the shore from the
point of turnaround to the point of overtaking the object?
in 30 min, the boat goes 1/2 * (9-4)=2.5km
in the same time, the object goes 2km
so the distance apart is 4.5km
Now, going downstream, the relative velocity between the boat and object is 9km, so time=reldistance/relvel=4.5km/(9km)=30min
total distance relative to shore:
distance up+distance down
2.5km+ rate(time)=
2.5km+ 13(1/2)=9km
a) Well, if the boat is turned around, it'll be going downstream this time, right? So, the boat's speed relative to the stream will be the sum of its own speed and the stream's speed: 9.0 km/h + 4 km/h = 13.0 km/h. Now, considering the object has been floating for 30 minutes, we can convert that time into hours by dividing it by 60, which gives us 0.5 hours. Therefore, it'll take the boat 0.5 hours to overtake the lost object.
b) To calculate the total distance, we can use the formula: Speed x Time = Distance. Since the speed of the boat, relative to the stream, is 13.0 km/h, and it took 0.5 hours to overtake the object, the distance covered will be: 13.0 km/h x 0.5 hours = 6.5 km. So, the boat will travel a total distance of 6.5 km relative to the shore from the point of turnaround to the point of overtaking the object.
To answer these questions, we need to determine the speed of the boat relative to the shore, both upstream and downstream.
(a) To calculate how long it will take for the boat to overtake the lost object after it is turned around, we need to find the speed of the boat relative to the shore when it is moving downstream (with the current).
Using the concept of relative speed, we can add the speed of the boat in still water and the speed of the river flowing downstream:
Boat speed downstream = Boat speed in still water + River speed
Boat speed downstream = 9.0 km/hr + 4 km/hr
Boat speed downstream = 13 km/hr
Since the boat is moving downstream, it will catch up to the object with a relative speed of 13 km/hr.
Now, we can convert the 30 minutes delay into hours:
Time delay = 30 minutes / 60 minutes/hour
Time delay = 0.5 hours
The time it will take to overtake the floating object can be calculated using the formula:
Time = Distance / Speed
Time = 0.5 hours (delay) / 13 km/hr (relative speed)
Time = 0.038 hours
Therefore, it will take approximately 0.038 hours (or 2.3 minutes) for the boat to overtake the lost object after it is turned around.
(b) The distance traveled by the boat relative to the shore from the point of turnaround to the point of overtaking the object can be calculated by multiplying the relative speed of the boat (13 km/hr) by the time it takes to overtake the object (0.038 hours).
Distance = Relative Speed * Time taken
Distance = 13 km/hr * 0.038 hours
Distance = 0.494 km (or 494 meters)
Therefore, the boat will travel a total distance of approximately 0.494 km relative to the shore from the point of turnaround to the point of overtaking the lost object.
To solve this problem, we need to break it down into different parts and analyze each part step by step.
First, let's calculate the speed of the boat relative to the water when it is traveling upstream. The boat's speed in still water is given as 9.0 km/hr. However, it is traveling against the flow of the river, which has a speed of 4 km/hr. So, the boat's speed relative to the water is 9.0 km/hr - 4.0 km/hr = 5.0 km/hr.
(a) If the boat is turned around, it will now be traveling downstream with the flow of the river. The speed of the boat relative to the water remains the same at 5.0 km/hr. Since the object was lost and not missed for 30 minutes, we can calculate the distance the object floated during this time.
Distance = Speed * Time
= 4.0 km/hr * (30 minutes / 60 minutes) (converting minutes to hours)
= 2.0 km
Now, let's calculate the time it will take for the boat to overtake the floating lost object. The boat's speed relative to the water is 5.0 km/hr, and it needs to cover a distance of 2.0 km.
Time = Distance / Speed
= 2.0 km / 5.0 km/hr
= 0.4 hours or 24 minutes
Therefore, it will take the boat 24 minutes to overtake the floating lost object.
(b) To calculate the total distance the boat will travel relative to the shore from the point of turnaround to the point of overtaking the object, we need to add the distance traveled while going upstream and the distance traveled while going downstream.
Distance upstream = Speed upstream * Time upstream
= 5.0 km/hr * 0.4 hr
= 2.0 km
Distance downstream = Speed downstream * Time downstream
= (9.0 km/hr + 4.0 km/hr) * 0.4 hr (since the boat's speed relative to the water is the sum of the boat's speed in still water and the river's flow speed)
= 13.0 km/hr * 0.4 hr
= 5.2 km
Total distance traveled relative to the shore = Distance upstream + Distance downstream
= 2.0 km + 5.2 km
= 7.2 km
Therefore, the boat will travel a total distance of 7.2 km relative to the shore from the point of turnaround to the point of overtaking the object.