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skelet666 [1.2K]
3 years ago
15

John has a boat that will travel at the rate of 15 kph in still water. he can go upstream for 35 km in the same time it takes to

go 140 km downstream. how fast is his boat traveling when he goes downstream? 22 kph 24 kph 26 kph
Physics
1 answer:
MA_775_DIABLO [31]3 years ago
5 0
Let F = the downstream speed of the water. 

<span>Then the boat's upstream speed is: 15 - F </span>
<span>The boat's downstream speed is: 15 + F </span>


<span>Assume both the journeys mentioned take T hours, then using "speed x time = distance" we get: </span>

<span>Downstream journey: (15 + F)T = 140 </span>
<span>Upstream journey: (15 - F)T = 35 </span>


<span>Add the two formulae together: </span>

<span>(15 + F)T + (15 - F)T = 140 + 35 </span>

<span>15T + FT + 15T - FT = 175 </span>

<span>30T = 175 </span>

<span>T = 35/6 </span>


<span>Use one of the equations to find F: </span>

<span>(15 + F)T = 140 </span>

<span>15 + F = 140/T </span>
<span>F = 140/T - 15 </span>
<span>F = 140/(35/6) - 15 </span>
<span>F = 24 - 15 </span>
<span>F = 9 </span>

<span>i.e. the downstream speed of the water is 9 kph </span>

<span>Therefore, the boat's speed downstream is 15 + F = 15 + 9 = 24 kph.
the answer is:                       *24kph*</span>
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A cart loaded with bricks has a total mass of 9.13 kg and is pulled at constant speed by a rope. The rope is inclined at 24.7 ◦
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Answer:

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Explanation:

Work (W) is defined as the point product of force (F) by the distance (d)the body travels due to this force.  

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F : force (N)

d : displacement (m)

α : angle between force and displacement

Newton's second law:

∑F = m*a Formula (2)  

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the cart on the ramp and the y-axis in the direction perpendicular to it.

Forces acting on the cart

W: Weight of the cart : In vertical direction

FN : Normal force : perpendicular to the floor

f : Friction force: parallel to the floor

T : tension Force,  inclined at  θ=24.7° above the horizontal

Calculated of the W

W= m*g

W= 9.13 kg* 9.8 m/s² = 89.47 N

x-y components o the  tension force (T)

Tx = Tcosθ = T*cos 24.7° (N)

Ty = Tsin θ = T*sin 24.7°  (N)

Calculated of the FN  

We apply the formula (2)  

∑Fy = m*ay ay = 0  

FN +Ty- W = 0  

FN = W-Ty  

FN =  89.47-T*sin 24.7°

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f = μk*FN

f =(0.597)*(  89.47-T*sin 24.7° )

f= 53.41-0.249T

Calculated of the tension force of the rope (f)

We apply the formula (2) :

∑Fx = m*ax  ,  ax= 0 ,because the speed of the cart  is constant

Tx - f = 0

T*cos 24.7°-( 53.41 - 0.249T )= 0

T*cos 24.7° + 0.249T = 53.41

(1.1575)T = 53.41

T= (53.41) / (1.1575)

T= 46.14 N

Work done on the cart by the rope

We apply the formula (1)

W=T*d *cosα

W= (46.14 N)*(15.1 m) *(cos24.7)

W = 632.97 (N*m) = 632.97 (J)

W = 0.63 KJ

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