It is 1:00 on a grandfather clock(a non-digital one), what time will it be when the minute hand and the hour hand form a 90 degree angle for the first time?

It is 1:00 on a grandfather clock(a non-digital one), what time will it be when the minute hand and the hour hand form a 90 degree angle for the first[/b'] time?

1:21:49.0909... (Time is in hours:minutes:seconds)

 

Of course, this assumes continuous movement of the minute and hour hands.

Yes. That's correct.

can you help me as to how did you calculate that

Let us say that this happens x seconds after 1 o'clock. Then the minute hand has moved (x seconds)/(3600 seconds in an hour)*(360 degrees per hour) = x/10 degrees, and the hour hand has moved (x seconds)/(3600 seconds in an hour)*(30 degrees per hour) = x/120 degrees. We have x/10 = x/120 + 120 (90 + 30, since we started at 1 o'clock) (+360k, k an integer,but in this case k = 0, since we are interested in the first case) and therefore, 11x/120 = 120, or x = 120*120/11 = 1309 + 1/11. Now, 1309 = 60*21 + 49, so it has passed 21 minutes and 49,090909... seconds.