Two walkers set off at the same time from a crossroad and walk along flat straight roads inclined to each other at 68 degrees.If they both walk at a speed of 6km/h,find their distance apart 10 minutes later.
1118 m
To find the distance apart between the two walkers 10 minutes later, we need to break down the problem into smaller steps.
Step 1: Convert the speed of the walkers from kilometers per hour to meters per minute.
Since 1 kilometer is equal to 1000 meters, we have:
Speed = 6 km/h * (1000 m/km) / (60 min/h)
Speed = 100 m/min
Step 2: Calculate the distance covered by each walker in 10 minutes.
Distance = Speed * Time
Distance = 100 m/min * 10 min
Distance = 1000 meters
Step 3: Calculate the horizontal distance covered by each walker.
Since the angle between the roads is 68 degrees, the horizontal distance covered by each walker can be calculated using trigonometry.
Horizontal distance = Distance * cos(angle)
Horizontal distance = 1000 m * cos(68 degrees)
Horizontal distance = 1000 m * 0.3746
Horizontal distance ≈ 374.6 meters
Therefore, the distance apart between the two walkers 10 minutes later is approximately 374.6 meters.
To find the distance between the two walkers, we can use the concept of relative velocity.
Let's assume that one of the walkers is moving towards the north, and the other walker is moving towards the east. We can break down their velocities into their northward and eastward components.
The vertical component of their velocity is given by:
Vertical velocity = Speed x sin(angle)
Vertical velocity = 6 km/h x sin(68°)
Similarly, the horizontal component of their velocity is given by:
Horizontal velocity = Speed x cos(angle)
Horizontal velocity = 6 km/h x cos(68°)
To find the distance between the walkers, we can use the Pythagorean theorem:
Distance = √((Vertical velocity x time)^2 + (Horizontal velocity x time)^2)
Since they walk for 10 minutes (10/60 hours), we can substitute this value into the equation:
Distance = √(((6 km/h x sin(68°)) x (10/60 hours))^2 + ((6 km/h x cos(68°)) x (10/60 hours))^2)
Now we can calculate the value of the distance.