Practice Escape Velocity in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Escape velocity is the minimum speed an object must have to escape a body's gravitational pull without further propulsion, ignoring air resistance.

It is the launch speed needed so gravity cannot pull the object back forever.

Showing a random 20 of 50 problems.

Example 1

easy
Does a 1 kg1\,\text{kg} object require the same escape speed from Earth as a 106 kg10^6\,\text{kg} rocket (ignoring air)?

Example 2

easy
A planet has the same density as Earth but twice the radius. By what factor is its escape velocity larger than Earth's?

Example 3

hard
From the Sun's surface (escape ve≈618v_e \approx 618 km/s), at what radius does escape speed drop to Earth's orbital speed ∼30\sim 30 km/s?

Example 4

easy
True or false: a body launched at escape speed will eventually fall back if gravity 'turns off' at infinity.

Example 5

medium
Jupiter has g≈24.8g \approx 24.8 m/s2^2 at radius r≈6.99×107r \approx 6.99\times 10^7 m. Compute its escape velocity.

Example 6

medium
A planet's escape velocity is 15 km/s15\,\text{km/s}. Find its low-orbit circular speed.

Example 7

medium
Find the minimum kinetic energy to escape for a 500 kg500 \text{ kg} probe where GM=4×1014GM = 4\times10^{14}, r=6.4×106 mr = 6.4\times10^6 \text{ m}.

Example 8

medium
A small asteroid has gsurface=0.01g_{surface} = 0.01 m/s2^2 and radius r=1000r = 1000 m. Estimate its escape velocity.

Example 9

challenge
A spacecraft escapes Earth (ve,⊕=11.2v_{e,\oplus} = 11.2 km/s) and then must reach interstellar space, escaping the Sun's gravity at Earth's orbit (ve,⊙≈42.1v_{e,\odot} \approx 42.1 km/s). Find the total launch speed from Earth's surface needed (ignoring Earth's orbital boost).

Example 10

easy
Find the escape velocity from a body where GM=4×1014GM = 4\times10^{14} and r=6.4×106 mr = 6.4\times10^6 \text{ m}.

Example 11

medium
Compare the escape velocities of two planets: planet A (MM, RR) and planet B (2M2M, 2R2R).

Example 12

medium
Find the escape velocity from the Moon: GM=4.9×1012GM = 4.9\times10^{12}, r=1.74×106 mr = 1.74\times10^6 \text{ m}.

Example 13

easy
Does escape velocity depend on the mass of the escaping object?

Example 14

easy
Escape velocity means the object escapes without further propulsion. Does gravity become zero after escape?

Example 15

medium
Find the escape velocity from a planet with GM=1imes1014GM = 1 imes10^{14} and radius r=5imes106extmr = 5 imes10^6 ext{ m}.

Example 16

challenge
If Earth were compressed to half its radius without changing its mass, by what factor would its escape velocity change?

Example 17

easy
A planet has the same mass as Earth but four times the radius. Find its escape velocity relative to Earth's 11.2 km/s11.2 \text{ km/s}.

Example 18

challenge
A probe is launched at 1.51.5 times Earth's escape velocity. Find its speed at infinity in terms of vev_e.

Example 19

medium
Using ve=2gRv_e = \sqrt{2 g R}, estimate Earth's escape velocity with g=9.8g = 9.8 m/s2^2 and R=6.4×106R = 6.4\times 10^6 m.

Example 20

medium
A body launched at exactly Earth's escape speed reaches r=4REr = 4R_E. Compare its speed there to Earth's escape speed.
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