Distance traveled by Hour and Minute hand in given Time interval
Given two numbers H and M which denotes the length of the hour and minute hand and two time intervals(say T1 & T2) in form of HH:MM, the task is to find the distance travelled by hour hand and minute hand between time T1 and T2.
Examples:
Input: H = 5, M = 7, T1 = “1:30”, T2 = “10:50”
Output:
Distance travelled by minute hand: 410.50144006906635
Distance travelled by hour hand: 24.434609527920614Input: H = 4, M = 5, T1 = “1:30”, T2 = “10:50”
Output:
Distance travelled by minute hand: 293.21531433504737
Distance travelled by hour hand: 19.54768762233649
Approach:
- Find the difference between the two time intervals T1 and T2 by using the approach discussed in this article.
- Change the time duration obtained above into minutes as:
Total Minutes = hours * 60 + minutes
- Since minute hand covers one rotation in 60 minutes therefore, number of rotations covered by minute hand(say rm) is given by
- Since hour hand covers one rotation in 60*12 = 720 minutes therefore, number of rotations covered by hour hand(say rh) is given by
- The total distance traverse by the hour hand is given by
- The total distance traverse by the minute hand is given by
Below is the implementation of the above approach:
Python
# Python program for the above approach import math # Function to remove ':' and convert# it into an integer def removeColon(s): if (len(s) == 4): s = s[:1]+s[2:] if (len(s) == 5): s = s[:2]+s[3:] return int(s) # function which find the difference# between time intervaldef diff(s1, s2): # Change string as 2:21 to 221 time1 = removeColon(s1) time2 = removeColon(s2) # Difference between hours hourDiff = time2 // 100 - time1 // 100 - 1; # Difference between minutes minDiff = time2 % 100 + (60 - time1 % 100) if (minDiff >= 60): hourDiff+= 1 minDiff = minDiff - 60 # Convert answer again in string # with ':' res = str(hourDiff) + ':' + str(minDiff) return res # Function for finding the distance travelled # by minute hand and hour handdef disTravel(T1, T2, M, H): # Find the duration between these time dur = diff(T1, T2) # Remove colom from the dur and # convert in int s = removeColon(dur) # Convert the time in to minute # hour * 60 + min totalMinute =(s//100)*60 + s % 100 # Count min hand rotation rm = totalMinute / 60; # Count hour hand rotation rh = totalMinute / 720; # Compute distance traveled by min hand minuteDistance = rm * 2* math.pi * M; # Compute distance traveled by hour hand hourDistance = rh * 2* math.pi * H; return minuteDistance, hourDistance # Driver Code # Given Time IntervalsT1 ="1:30"T2 ="10:50" # Given hour and minute hand length H = 5M = 7 # Function CallminuteDistance, hourDistance = disTravel(T1, T2, M, H) # Print the distance traveled by minute# and hour handprint("Distance traveled by minute hand: " ,minuteDistance)print("Distance traveled by hour hand: " ,hourDistance ) |
Distance traveled by minute hand: 410.50144006906635 Distance traveled by hour hand: 24.434609527920614
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