So, im not sure how to do this question:
Two roads diverge at a 52° angle. Two bike riders take separate routes at 17 km/h and 24 km/h. How far apart are they after 2 hours?
could i get some help please??
thanks!
After 2 hours, the first rider went 34 km and the 2nd rider went 48 km
the angle between them is 52°
Make a sketch and use the cosine law:
x^2 = 34^2 + 48^2 - 2(34)(48)cos52°
= 1450.48...
x = √1450.48... = appr 38.085
or 38.1 km , like their answer
Thank you very much!
Sure! I can help you with that.
To solve this problem, we can use the concept of relative velocity.
Step 1: Convert the speeds from km/h to km/min.
- The speed of the first bike rider is 17 km/h. To convert it to km/min, divide by 60 since there are 60 minutes in an hour.
17 km/h = 17 km/60 min ≈ 0.283 km/min
- The speed of the second bike rider is 24 km/h. Converting to km/min:
24 km/h = 24 km/60 min ≈ 0.4 km/min
Step 2: Calculate the horizontal and vertical distances covered by each bike rider.
- The first bike rider travels for 2 hours at a speed of 0.283 km/min. Therefore, the horizontal distance covered by this rider will be:
Horizontal distance = Speed x Time = 0.283 km/min x 120 min = 33.96 km
- The vertical distance covered will be the same for both bike riders since they are traveling at the same angle. So, the vertical distance covered by each bike rider after 2 hours is:
Vertical distance = Speed x Time = 0.4 km/min x 120 min = 48 km
Step 3: Calculate the distance between the two bike riders.
- To find the distance between them, we can use the Pythagorean theorem. The two distances we calculated are the two sides of a right-angled triangle, and the distance between the bike riders is the hypotenuse.
Distance between bike riders = √((Horizontal distance)^2 + (Vertical distance)^2)
= √((33.96 km)^2 + (48 km)^2)
≈ √(1152.3216 km^2 + 2304 km^2)
≈ √3456.3216 km^2
≈ 58.8 km
Therefore, after 2 hours, the two bike riders will be approximately 58.8 km apart.
Certainly! To find out how far apart the two bike riders are after 2 hours, we will need to calculate the distances each rider has traveled.
Let's start by calculating the distance traveled by the first rider. The formula to calculate distance is: distance = speed × time.
For the first rider, the speed is given as 17 km/h, and the time is 2 hours. Therefore, the distance traveled by the first rider is:
Distance_1 = Speed_1 × Time = 17 km/h × 2 hours = 34 km.
Now let's calculate the distance traveled by the second rider. Similarly, the speed of the second rider is given as 24 km/h, and the time is also 2 hours. Therefore, the distance traveled by the second rider is:
Distance_2 = Speed_2 × Time = 24 km/h × 2 hours = 48 km.
Now that we know the distances traveled by each rider, we can find the distance between them. This can be done using trigonometry since we know the angle between the two roads and the distances they have traveled.
Using the angle of 52°, we can apply the sine function to find the "opposite" side of the triangle formed by the two riders' paths.
Distance_apart = Distance_2 × sin(angle) = 48 km × sin(52°) ≈ 37.122 km.
Therefore, after 2 hours, the two bike riders are approximately 37.122 km apart.
I hope this helps! Let me know if you have any further questions.