5. Fred and Pete are riding their bicycles along two straight footpaths that lea

Question

5. Fred and Pete are riding their bicycles along two straight footpaths that lead to a junction. They are both riding towards the junction. The angle between the two paths, at the junction, is 70°. Fred is riding an old red bicycle with a rear wheel diameter of 0.5 m. This wheel is turning at a constant speed of 152.79 RPM. Fred will reach the junction in 5 seconds. Pete is riding a new blue bicycle at a speed of 2 m/s and is 15 m away from the junction. a) Will the two boys collide at the junction? If not, by how much time will they miss each other? b) From Fred's viewpoint (his corner of the triangle), what is the angle between the junction and Pete?

Explanation / Answer

a) Two boys will collide if they reach at the same time on the junction.

Pete will reach in 15/2 = 7.5 seconds

Fed reaches in 5 sec

They miss each other by 2.5 sec.

b) Linear velocity of Fred : v = r*w = r × RPM × 0.10472 = 8 m/sec

Distance bewteen Fred and junction = 8* 5 =40mt

So, we have a triangle with two sides 40mt and 15mt and one angle with 70 deg

We find the third side by cosine rule: c^2 = a^2 +b^2 -2abcosC

= 40^2 + 15^2 -2*40*15cos70

On solving c = 37.6 mt

Now applying sine rule to find the angle between  junction and Pete

40/sinA = 37.6/sin70

sinA = 1

Angle A = 90 degrees (angle between  junction and Pete)

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