The escape velocity of a projectile on the surface of the earth is 11.2km/s a body is projected out with twice this speed what is the speed of the body gar away from the earth ignore the sun. And any planet
Answers
Given ,
escape speed on the earth's surface (Ve) = 11.2 km/s
speed of projection of the body (v) = 3Ve = 3×11.2 = 33.6 km/s
Let v and v' be the speed of the body at the time of projection and at a point far from the earth.
Initial K.E of the body = 1/2mv²
Initial Gravitational PE of the body = -GMem/Re
Where, Me , Re are the mass , radius respectively.
At very far from the earth surface .
KE of the body = 1/2mv²
Gravitational PE of the body = 0
A/c to law of conservation of energy .
Total energy at the point of projection = total energy at very far from the earth's surface.
1/2mv² + (-GMem/Re) = 1/2mv'²
1/2 mv'² = 1/2mv² - GMem/Re
If Ve is the escape velocity , then,
1/2 mVe² = GMem/Re
1/2mv'² = 1/2mv² - 1/2mVe²
v'² = v - Ve²
= (3Ve)² - Ve²
= 8Ve²
v'² = 8Ve²
v' = 2√2Ve
v = 2 × 1.414 × 11.2 km/s
= 31.68 km/s
Hence, speed of the body at far away from the earth = 31.68 km/s