Topic - Kinematics
Answers are written I need Explanation.
Answer fully! No spams!
Best to be marked as Brainliest!
Stars and mod please answer my question!!!....
Answers
Answer :
Given, BC = 120 m
Let
u be the velocity of the water flow
v be the velocity of man w.r.t river
w be the width of the river
Case - (i) :
The man swims perpendicular to the bank and reaches point C in 10 minutes.
time, t₁ = 10 min = 10 × 60 sec = 600 sec
Drift, BC = 120 m
Speed = distance/time
⇒ Speed of the water flow = BC / time
⇒ u = 120 / 600
⇒ u = 0.2 m/s
⇒ u = 0.2 × 18/5 kmph
⇒ u = 0.72 kmph [Ans]
Also, width of the river = speed of the man w.r.t river × t₁
w = v (600)
w = 600v ---[1] (units of 'v' to substitute here is m/s)
Case - (ii) :
The man swims at an angle θ to AB and reaches B in 12.5 minutes
time, t₂ = 12.5 min = 12.5 × 60 sec = 750 sec
- The component of the velocity of man along the width of the river is vcosθ (as he swims at an angle θ to AB)
w = v cosθ × t₂
w = vcosθ × 750
600v = vcosθ × 750
cosθ = 600/750
cosθ = 4/5 = adjacent side/hypotenuse
In a right angled triangle,
hypotenuse² = adjacent side² + opposite side²
5² = 4² + opposite side²
opposite side² = 25 - 16
opposite side² = 9
opposite side = √9
opposite side = 3
sinθ = opposite side/hypotenuse
sinθ = 3/5
θ = sin⁻¹ (3/5) [Ans]
- The component of the velocity of man along the bank of the river is vsinθ
vsinθ = u (so that drift is minimum)
v (3/5) = 0.72 kmph
v = 0.72 × 5/3
v = 0.24 × 5
v = 1.2 kmph [Ans]
v = 1.2 × 5/18 m/s = 1/3 m/s
Substitute in equation [1],
w = 600v
w = 600 (1/3)
w = 200 m [Ans]
___________________________
9. A river of flows at 5ms⁻¹ it is 200m width. A man crosses the river in the shortest time of 25s. If there is no flow and swims with the same velocity, the time taken to cross the river is 25 sec
Shortest time condition :
The man reaches the other side of the river in the shortest time when he swims perpendicular to bank.
time = width of the river/velocity of the man
velocity of the man = 200/25
velocity of the man = 8 m/s
If there is no flow, velocity of the water flow is 0 m/s
time taken to cross the river = width of the river / velocity of the man
required time = 200/8
required time = 25 sec
∴ The time taken to cross the river is 25 sec
Answer:
setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,0){4}}\put(0,2){\line(1,0){4}}\put(1.8,0){\circle*{0.15}}\put(1.7,-0.5){\sf A}\put(1.8,2){\circle*{0.15}}\put(1.7,2.2){\sf B}\multiput(1.8,0)(0,0.3){7}{\line(0,1){0.2}}\put(1.8,0){\line(1,1){2}}\put(1.5,0.4){$ \theta $}\put(3.6,2.2){\sf C}\put(1.8,0){\vector(-1,1){1}}\put(0.3,2.2){\vector(1,0){1}}\put(0.7,2.3){\sf u}\put(0.6,1){\sf v}\end{picture}
Given, BC = 120 m
Let
u be the velocity of the water flow
v be the velocity of man w.r.t river
w be the width of the river
Case - (i) :
The man swims perpendicular to the bank and reaches point C in 10 minutes.
time, t₁ = 10 min = 10 × 60 sec = 600 sec
Drift, BC = 120 m
Speed = distance/time
⇒ Speed of the water flow = BC / time
⇒ u = 120 / 600
⇒ u = 0.2 m/s
⇒ u = 0.2 × 18/5 kmph
⇒ u = 0.72 kmph [Ans]
Also, width of the river = speed of the man w.r.t river × t₁
w = v (600)
w = 600v ---[1] (units of 'v' to substitute here is m/s)
Case - (ii) :
The man swims at an angle θ to AB and reaches B in 12.5 minutes
time, t₂ = 12.5 min = 12.5 × 60 sec = 750 sec
The component of the velocity of man along the width of the river is vcosθ (as he swims at an angle θ to AB)
w = v cosθ × t₂
w = vcosθ × 750
600v = vcosθ × 750
cosθ = 600/750
cosθ = 4/5 = adjacent side/hypotenuse
In a right angled triangle,
hypotenuse² = adjacent side² + opposite side²
5² = 4² + opposite side²
opposite side² = 25 - 16
opposite side² = 9
opposite side = √9
opposite side = 3
sinθ = opposite side/hypotenuse
sinθ = 3/5
θ = sin⁻¹ (3/5) [Ans]
The component of the velocity of man along the bank of the river is vsinθ
vsinθ = u (so that drift is minimum)
v (3/5) = 0.72 kmph
v = 0.72 × 5/3
v = 0.24 × 5
v = 1.2 kmph [Ans]
v = 1.2 × 5/18 m/s = 1/3 m/s
Substitute in equation [1],
w = 600v
w = 600 (1/3)
w = 200 m [Ans]
___________________________
9. A river of flows at 5ms⁻¹ it is 200m width. A man crosses the river in the shortest time of 25s. If there is no flow and swims with the same velocity, the time taken to cross the river is 25 sec
Shortest time condition :
The man reaches the other side of the river in the shortest time when he swims perpendicular to bank.
time = width of the river/velocity of the man
velocity of the man = 200/25
velocity of the man = 8 m/s
If there is no flow, velocity of the water flow is 0 m/s
time taken to cross the river = width of the river / velocity of the man
required time = 200/8
required time = 25 sec
∴ The time taken to cross the river is 25 sec