By the velocity, they will travel 6.875 m and the dog catches the man at 2.08s.
We need to know about velocity to solve this problem. Velocity can be determined as the distance traveled divided by time interval. It can be written as
v = s / t
where v is velocity, s is distance and t is the time interval.
From the question above, we know that.
v man = 1.5 m/s
v dog = 3.3 m/s
to = 2.5s
Determine the distance traveled by man when the dog waits
so = vman . to
so = 1.5 x 2.5 = 3.75 m
Find the man's total distance
total distance = distance after dog run + distance when the dog waits
total distance = vman . t + 3.75
We know that the total distance by man's will be caught by the dog, Thus
total distance = vman . t + 3.75
v dog . t = 1.5t + 3.75
3.3t = 1.5t + 3.75
1.8t = 3.75
t = 2.08 s
Find total distance
total distance = vdog . t
total distance = 3.3 x 2.08
total distance = 6.875 m
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