A rocket is launched straight up from the earth’s surface at a speed of 1.70×104 m/s.?

A rocket is launched straight up from the earth’s surface at a speed of 1.70×104 m/s.

What is its speed when it is very far away from the earth?

Thank you!!

Initial Kinetic Energy (KE) of the rocket = 1/2*mv^2 = (1.445 x 10^8) * m

Initial potential energy (PE) = -GMm / R

= – (6.67 * 10^-11) (6 * 10^24) m / (6.4 * 10^6)

= (- 6.25 * 10^7) * m

Total initial energy = KE + PE = (8.2 x 10^7 )* m

From Conservation of Energy,

Total Initial Energy = Total Final Energy

So

Total Final Energy = 8.2 x 10^7 * m

Final PE = 0 (Put r = infinity in the expression for PE)

So

Final KE = 8.2 * 10^7 * m

1/2*m*v^2 = 8.2 * 10^7 * m

v = 1.28 x 10^4 m/s

Hope your enjoying Clemson, just did the problem myself (;

Source(s): student

A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 m/s .