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September 8th, 2018, 11:16 PM   #1
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Dynamics; Kinematics (further math)

Hello guys, it's been long since I posted here due to the fact that I'm learning....I just want to present some question to this forum today... which consist of
1. Dynamics
2. Vector
3. Trigonometry
I have no idea on both dynamics and vector... Believe me. I just want the mathematicians of this forum to solve for me. I would be grateful and the question I'll post today must consist of diagrammatic representation (pardon me, but it is compulsory)....

Dynamics....
The speed of a boat in still water is 5m/s. The boat heads straight across a river which is 300m wide but actually travels at an angle of 60 degree to the bank
(a) Calculate and correct to 2 d.p.
1. The speed of the boat relative to the ground
2. The speed of the current
(b) what is the time taken by the boat to cross the river?
Guys, please I have 0% knowledge of dynamics, therefore hints are not useful... you can even send attached pics solution. I would be grateful.

Last edited by skipjack; September 9th, 2018 at 04:18 AM.
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September 9th, 2018, 12:45 PM   #2
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The boat's rate of progress across the river isn't affected by the speed of the current, so the time the boat takes to cross the river is 300/5 seconds = 60 seconds.

Let c m be the distance downstream that the boat is taken by the current.
River.PNG
By Pythagoras, c² + 300² = (2c)², so c = 100√3.

Hence the speed of the current is c/60 m/s = 2.89 m/s to 2 d.p.

The speed of the boat relative to the ground is 2c/60 m/s = 5.77 m/s to 2 d.p.
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