Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it

Question

Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it take for the two cars to meet?


plz solve with explanation.

Answer 1

Hour and a Half

Answer 2

Depends...you left out a lot of information needed to really answer this.

For example:

Did they initially turn toward each other or away. If they turn towards each other and are positioned just right, they could collide earlier rather than later. If they turn away, they will collide later as they would eventually be coming back because they are going in circles. But, again, whether they collide or not depends on where they started from. S = 15 km is not sufficient information, we need to know where one car is relative to the other when they start their turns (e.g., one is north of the other, or east, or 110 degrees, etc.).

Are they both turning at the same radius of turn, the same angular velocity? Tangential velocity (50 and 40 kph) is V = WR and v =wr; V/v = (WR/wr); where W and w are the angular velocities and R and r are the radii of turn for the 50 and 40 kph turns respectively. So, as you can see if R = r, the angular velocities are V/v = W/w > 1.0 But if W = w, the radii are V/v = R/r > 1.0 for the given tangential velocities.

I'm going to make some assumptions. The cars are oriented north-south from each other when S = 15 km. Both are at the top of their turn circles (12 o'clock position) when they turn in opposite directions, the 50 kph north car initially turns west (counter clockwise), the 40 kph south car initially turns east (clockwise). They turn at the same angular velocity; so W = w and V/v = R/r; so that R = (V/v) r = 5/4 r.

Thus S = 15 km, the distance between the two cars when they both are at the twelve o'clock position. Therefore we have S = 2R, when the 50 kph car is just starting from its 12 o'clock position on its circle in the north and the 40 kph car is just starting from its 12 o'clock position on its circle in the south. So R = S/2 = 15/2 km and r = 4/5 R = 60/10 = 6 km.

Given the assumption W = w, their angular velocities are the same, both cars will reach the mirror images of the relative angular positions. By mirror images, I mean we take into account that, although the angular speeds are the same (w = W), the angular velocities are actually in opposite direction; so that w = -W when considered as velocities.

For example, when the north car, going counter CC, is at 270 degrees (zero degrees is due North on both circles) on its turn circle, the south car, going CC, will be at 090 degrees on its circle. Thus, they both will be at 180 degrees, the southern most poistion, at the same time on their respective circles but coming from opposite directions. At which time they will be s = 2r = 12 km apart...and that's the closest they will ever get as long as W = w (their angular velocities are the same) and they both start from the top of their turn circles.

On the other hand, if the 50 kph car starts from the 12 o'clock position, and the 40 kph car starts from the 6 o'clock position of their respective turn circles, and S = 15 = 2R + 2r = D + d; where D and d are the turn circle diameters...they will collide after traveling C/2 = pi D/2 = pi R and c/2 = pi d/2 = pi r or halfway around their respective circles.

Why? Because they are travelling at W = w, the same angular velocities by my assumption. So the north car will be at 6 o'clock on its circle when the south car is at its 12 o'clock position. And when the 50 kph car is going counter CC and the 40 kph car is also going counter CC this time (because it initially turns east as before, but from the 6 o'clock position instead of the 12 o'clock), they will end up after going halfway around their circles (C/2 and c/2) at the same geographical place at the same time...a collision. And that elapsed time, from start, is just distance/velocity = C/2//V = c/2//v = 2 pi r/2//v = pi r/v = 6pi/40 ~ 19 km/40 kph ~ 1/2 hour = 30 minutes.

So, as I said earlier...the answer to your question is...it depends. It depends on a lot of information you did not provide. I gave you two examples: one where they'd never collide and the other where they'd collide after about 30 minutes travel on their respective turn circles.

Answer 3

The easiest way to look at this, is to notice that, if you are in one car, the other car appears to be approaching you at a relative speed of 90 kph (that is, 40kph + 50kph).

So, how long does it take to cover 15 km at a speed of 90 kph?