Duas esferas A e B de massa m e 2m respetivamente são lançadas verticalmente para cima. A esfera A é lançada a partir do solo com velocidade de valor 10 ms-1, e a esfera B de uma altura de 2,0m, com velocidade de valor 6ms-1. Despreze o efeito da resistência do ar, e considere o referencial unidimensional 0Y, com sentido positivo de cima para baixo. Utilizando as Leis da Cinemática, determine a razão entre a altura máxima atingida pela esfera B e a altura máxima atingida pela esfera A.

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Ответ:

moneykingmarco079

17.05.2020

Physics

$\frac{dh}{dt}=10\sqrt{2}$ =14.14 [cm/min]

Explanation:

If we have an isosceles right triangle we can use the Pythagoras theorem to find the hypotenuse:

$h^{2}=x^{2}+x^{2}=2x^{2}$ (1)

$h=\sqrt{2x^{2}}=x\sqrt{2}$ (2)

From equation (2) let's take the derivative with respect to time (t):

$\frac {dh}{dt}=\frac {dx(\sqrt {2})}{dt}$

$\frac {dh}{dt}=\frac {dx}{dt}\sqrt {2}$

dx/dt is the increasing rate of the triangle legs, it is dx/dt = 10 [cm/min].

$\frac{dh}{dt}=10\sqrt{2}$ =14.14 [cm/min] (3)

(3) is the hypotenuse increasing in length, and when x = 2 cm, using equation (2), h will be equal to 2.83 cm.

Hava a nice day!

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