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3 years ago

In Europe, gas cost approximately €0.98 per liter. How many dollars($) per gallon is this? using a factor method

Physics

1 answer:

bixtya [17]3 years ago

5 0

Answer:

€0.98 per liter = 4.377 doller per gallon

Explanation:

It is given that, In Europe, gas cost approximately €0.98 per liter. We need to convert it into dollars($) per gallon.

We know that, 1 euro = 1.18 United States Dollar

1 litre = 0.264172 US gallon

Cost of gas in Europe is €0.98 per liter.

$0.98\ \text{euro/ liter}=\dfrac{0.98\times 1.18\ \text{doller}}{0.264172\ \text{gallon}}\\\\=4.377\ \text{doller/gallon}$

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2 years ago

A 40 kg girl and an 8.4 kg sled are on the surface of a frozen lake, 15 m apart. By means of a rope, the girl exerts a 5.2 N for

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Answer:

(a) $a_s=0.62\frac{m}{s^2}$

(b) $a_s=0.13\frac{m}{s^2}$

Explanation:

(a) According to Newton's second law, the acceleration of a body is directly proportional to the force exerted on it and inversely proportional to it's mass.

$a_s=\frac{F}{m_s}\\a_s=\frac{5.2N}{8.4kg}\\a_s=0.62\frac{m}{s^2}$

(b) According to Newton's third law, the force that the sled exerts on the girl is equal in magnitude but opposite in the direction of the force that the girl exerts on the sled:

$a_g=\frac{F}{m_g}\\a_g=\frac{5.2N}{40kg}\\a_g=0.13\frac{m}{s^2}$

$x_f=x_0+v_0t \pm \frac{at^2}{2}$

For the girl, we have $x_0=0$ and $v_0=0$ . So:

$x_f_g=\frac{a_gt^2}{2}(1)$

For the sled, we have $v_0=0$ . So:

$x_f_s=x_0_s-\frac{a_st^2}{2}(2)$

When they meet, the final positions are the same. So, equaling (1) and (2) and solving for t:

$x_0_s-\frac{a_st^2}{2}=\frac{a_st^2}{2}\\t^2(a_g+a_s)=2x_0_s\\t=\sqrt{\frac{2x_s_0}{a_g+a_s}}\\t=\sqrt{\frac{2(15m)}{0.13\frac{m}{s^2}+0.62\frac{m}{s^2}}}\\t=6.32s$

Now, we solve (1) for $x_f_g$

$x_f_g=\frac{0.13\frac{m}{s^2}(6.32s)^2}{2}\\x_f_g=2.6m\\x_f=2.6m$

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3 years ago

In Europe, gas cost approximately €0.98 per liter. How many dollars($) per gallon is this? ​ using a factor method

In Europe, gas cost approximately €0.98 per liter. How many dollars($) per gallon is this? using a factor method