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antiseptic1488 [7]
3 years ago
15

Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject materia

l as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg and a radius of 1821 km. For this calculation, ignore any variation in gravity over the 500 km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?
Physics
1 answer:
alisha [4.7K]3 years ago
6 0

Answer:

91.54 km

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

r = Radius of Io = 1821000 m

m = Mass of the Io =  8.93 × 10²² kg

H_i = 500000 m

g = Acceleration due to gravity on Earth = 9.81 m/s²

Acceleration due to gravity on Io

g_i=\frac{GM}{r^2}\\\Rightarrow g_i=\frac{6.67\times 10^{-11}\times 8.93\times 10^{22}}{1821000^2}\\\Rightarrow g_i=1.796\ m/s^2

H_e=\frac{v^2}{2g}

H_i=\frac{v^2}{2g_l}

Dividing the above equations we get

\frac{H_e}{H_i}=\frac{\frac{v^2}{2g}}{\frac{v^2}{2g_i}}\\\Rightarrow \frac{H_e}{H_i}=\frac{g_i}{g}\\\Rightarrow \frac{H_e}{H_i}=\frac{1.796}{9.81}\\\Rightarrow H_e=H_i\times \frac{1.796}{9.81}\\\Rightarrow H_e=500000\times \frac{1.796}{9.81}\\\Rightarrow H_e=91539.245\ m=91.54\ km

The material would go 91.54 km on earth if it were ejected with the same speed as on Io.

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(b)  it’s possible for a diver to enter the water with the velocity of 25 m/s if he has initial velocity of 14.4 m/s. The upward initial velocity can’t be physically attained

Explanation:

(a)

To find the final velocity V_{f} for an object traveling distance h taking the initial vertical component of velocity as V_{i} the kinematics equation is written as

V_{f}^{2}=V_{i}^{2}+2ah where a is acceleration

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Therefore, the divers enter with a speed of 20.4 m/s

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(b)

The divers can enter water with a velocity of 25 m/s only if they have some initial velocity. Using the kinematic equation

V_{f}^{2}=V_{i}^{2}+2gh

Since we have final velocity of 25 m/s

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Therefore, it’s possible for a diver to enter the water with the velocity of 25 m/5 if he has initial velocity of 14.4 m/s

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