Please help me with these two related rates problems! Two cars approach an inter

Question

Please help me with these two related rates problems!

Two cars approach an intersection, one heading east at 30 km/h and the other heading south at 40 km/h. At what rate are the two cars approaching each other at the instant when the first car is 100 m from the intersection and the second car is 75 m from the intersection? A Ferris wheel is 50 ft in diameter and its center is located 30 ft above the ground. If the wheel rotates once every 2 min, how fast is a passenger rising when he is 42.5 ft above the ground?

Explanation / Answer

Q9)-

first we have to change the velocity in m/s, So-

30 km/h = (5/18)* 30 = 8.34 m/s

And 40 km/h = (5/18)* 40 = 11.12 m/s-

then -

angle between first car and X-axis is tan-1(75/100) = 36.86o

so the second car and Y-axis angle will be (90-36.86) = 53.13o

then-

rate of approaching = (V1cos(36.86)) + (-V2cos(53.13))

= 8.34*(0.8) + (-11.12*0.6)

= 6.672 - 6.672

= 0

this shows that these two car will not be approch each other ever.

Q10)-

First we convert the rotation per min to rad/sec

So-

0.5 rotaion per min = 0.052 rad/sec = Omega

then-

person rotating velocity = Omega*R

= 0.052*(7.62) (Here 25 feet = 7.62m)

= 0.396 m/s

angle between velocity and vertical axis is = 180 - sin-1( (42.5-30) / 25 )

= 180-30 = 150o

then rising rate = 0.396*cos(150)

= -0.342 m/s

Thank you !!! Have fun

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