Question

two cyclist A and B start from the junction of two roads inclined at 90°,the ratio of their velocities being 3:4.find the ratio of the rate at which two cyclist are seperating with the velocity of A.

Answer 1

HEY DEAR HERE IS YOUR ANSWER ✌ ✌❤ ❤

Since the two cyclists have a 3:43:4 ratio of velocities, we assume they are 3v,4v correspondingly.

Then, the distance of cyclist A from the intersection is given by d1=3vt.

In the same way, the distance of cyclist B from the intersection is given by d2=4vt.

By Pythagorean's theorem we know the distance between the two cyclists is 
d= √d² 1 +d² 2−−−−−−√=5vtd=d12+d22=5vt.

Thus, the rate at which two cyclists are separating can be found by taking derivative of dd with respect to time tt. ddt5vt=5vddt5vt=5v

Therefore, the ratio ratio of the rate at which two cyclists are separating with the velocity of A should be 5v3v=535v3v=53. You got it!

Answer 2

Answer:

HEY DEAR HERE IS YOUR ANSWER ✌ ✌❤ ❤

Since the two cyclists have a 3:43:4 ratio of velocities, we assume they are 3v,4v correspondingly.

Then, the distance of cyclist A from the intersection is given by d1=3vt.

In the same way, the distance of cyclist B from the intersection is given by d2=4vt.

By Pythagorean's theorem we know the distance between the two cyclists is 

d= √d² 1 +d² 2−−−−−−√=5vtd=d12+d22=5vt.

Thus, the rate at which two cyclists are separating can be found by taking derivative of dd with respect to time tt. ddt5vt=5vddt5vt=5v

Therefore, the ratio ratio of the rate at which two cyclists are separating with the velocity of A should be 5v3v=535v3v=53.

You got it!