A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of 5 m/s at an angle of 120with the flow.The speed of the flow must be.
Answers
Answer:
Let the velocity of of man be Vm and velocity of flow of water Vw as shown in figure.
First method:-
If we divide Vm in two components as it is a vector quantity, Then,
Horizontal component Vm.cos120° will be equal to Vw,
Vm.cos120° = Vw
Vw = Vm.cos120°
Vw = - 5 × 1/2
Vw = - 2.5
|Vw| = 2.5 m/s
Second Method,
In ΔABC,
sin30° = AB/AC
1/2 = Vw/Vm
Vw = 5 × 1/2
Vw = 2.5 m//s
Explanation:
Answer:
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Let mth term of AP be ‘Am’ and nth term of AP be ‘An’
Therefore, Am = a+ (m-1)d=1/n ….(i)
An = a+(n-1)d=1/m ….(ii)
Subtracting equation (ii) from (i)
d[(m-1)-(n-1)] = 1/n-1/m,
d(m-n) = (m-n)/mn,
d = 1/mn ….(iii)
Substituting equation (iii) in (i)
a+(m-1)/mn = 1/n,
a = 1/n[1-(m-1)/m],
a = 1/mn ….(iv)
Now Amn i.e the mnth term of AP = a+(mn-1)d,
Substitute equation (iii) and (iv) in Amn,
1/mn+(mn-1)/mn = 1/mn[1+(mn-1)] = mn/mn = 1,
then the mn term = 1
sum of mn term :-
Amn = mn/2 ( 2/mn + (mn-1)1/mn)
= 1 + (mn)/2 - 1/2
= mn /2 + 1/2
= 1/2 (mn + 1)
Explanation: