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2 years ago

Solve for u. m/u^2+r=−k−y

Mathematics

1 answer:

mylen [45]2 years ago

7 0

9514 1404 393

Answer:

u = ±√(-m/(k+r+y))

Step-by-step explanation:

Subtract r, rearrange, then take the square root.

$\dfrac{m}{u^2}+r=-k-y \qquad\text{given}\\\\ \dfrac{m}{u^2}=-k-y-r\\\\-\dfrac{m}{k+r+y}=u^2\\\\ \boxed{u=\pm\sqrt{-\dfrac{m}{k+r+y}}}$

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Answer:

Step-by-step explanation:

The motion of the dolphin is quadratic

i.e y=-16t²+20t

To get the maximum height the dolphin will reach

We need to find the point of inflexion. i.e dy/dt=0

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Then set dy/dt=0

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Then, -32t=-20

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Then substitute t=0.625 into y

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Then the maximum height the dolphin can reach is 6.25ft

Using discriminant

Formular method

y=-16t²+20t

So the dog height y<7

y=-16t²+20t <7

-16t²+20t-7<0

a=-16, b= 20. c=-7

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Using the a, b and c direct for the discriminant

D=b²-4ac

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Therefore,

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We cannot do anything to a and b it is already given

a=-16, b=20

(20)²-4(-16c)>0

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64c>-400

Then

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Divide both side by - and the inequality sign will change

Therefore -c<6.25

So the dog height y<6.25

y=-16t²+20t <6.25

Therefore the maximum height is 6.25.

If it is greater than that then, we are going to have a complex root movement which is not possible for the dolphin .

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