Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.1×104 m/s when at a distance of 2.5×1011 m from the center of the sun, what is its speed when at a distance of 4.9×1010 m .Express your answer using two significant figures.

v_f = 6.92 x 10^(4) m/s

Explanation:

From conservation of energy,

E = (1/2)mv² - GmM/r

Where M is mass of sun

Thus,

E_i = E_f will give;

(1/2)mv_i² - GmM/(r_i) = (1/2)mv_f² - GmM/(r_f)

m will cancel out to give ;

(1/2)v_i² - GM/(r_i) = (1/2)v_f² - GM/(r_f)

Let's make v_f the subject;

v_f = √[(v_i)² + 2MG((1/r_f) - (1/r_i))]

G is Gravitational constant and has a value of 6.67 x 10^(-11) N.m²/kg²

Mass of sun is 1.9891 x 10^(30) kg

v_i = 2.1×10⁴ m/s

r_i = 2.5 × 10^(11) m

r_f = 4.9 × 10^(10) m

Plugging in all these values, we have;

v_f = √[(2.1×10⁴)² + 2(1.9891 x 10^(31)) (6.67 x 10^(-11))((1/(4.9 × 10^(10))) - (1/(2.5 × 10^(11)))] 20.408 e12

v_f = √[(441000000) + 2(1.9891 x 10^(30)) (6.67 x 10^(-11))((16.408 x 10^(-12))]

v_f = √[(441000000) + (435.38 x 10^(7))

v_f = 6.92 x 10^(4) m/s

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.