1 out of 7 attempts Assistance Round your final answer to three significant figu

Question

1 out of 7 attempts Assistance Round your final answer to three significant figures. ith mass of 143 kg is launched straight up from the Earth's surface with anCheek My Work A projectile with mass of 143 kg is launched straight up from the Earth's surface with an initial speed vi. What magnitude of v, enables the projectile to just reach a maximum height of SRE. measured from the center of the Earth? Ignore air friction as the projectile goes through the Earth's atmosphere, and answer in units of km/s View Hint View Question Show Me Guided Solution Practice This Question Print Question Help Report a Problem km/s

Explanation / Answer

since the answer is independent of the mass as you will see in the following calculations.
In this problem, since the value of acceleration of gravity changes with height, it can best be solved using energy balance.

(potential energy + kinetic energy) at launch =

(potential energy + kinetic energy )at max ht

at start: KE=1/2mv^2 and potential energy = -GMm/RE where G is newtonian grav cst, M is mass of Earth, m is mass of projectile, RE is distance from center of earth

at max height, KE=0 and PE = -GMm/8RE

=> (1/2) mvi^2 - GmM/R = - GmM/(8R)
=> (1/2) vi^2 = (GM/R) * (1 - 1/8)
= >(1/2) vi^2= (7/8) (GM/R^2) * R
= >(1/2) vi^2=  (7/8) gR
= > vi^2 = (7/4) * (9.81 x 10^-3) * 6878.1 km/s ... [g = 9.81 m/s^2 = 9.81 x 10^-3 km/s^2]
= > vi^2= 118.07

=> Vi = 10.86 km/s

=> vi = 10.39 km/s.

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