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maniacp08
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Gravity -- maximum height
An object is projected upward from the surface of the Earth with an initial speed of 3.7 km/s. Find the maximum height it reaches.
m
Ive used the Energy conservation
Kf + Uf = Ki + Ui
1/2 mvf^2 - G*M_e*m/rf = 1/2 mvi^2 - G*M_e*m/ri
= 0 - G*M_e*m/rf = 1/2 mvi^2 - G*M_e*m/R_e
R_e = radius of Earth = 6.37 x 10^6m
M_e = mass of Earth = 5.98 x 10^24kg
G = 6.67 x 10^-11 N*m^2/kg^2
1/radius_f = -Vi^2/2*G*M_e + 1/R_e
1/radius_f = (-3700 m/s)^2 / 2(6.67 x 10^-11)(5.98 x 10^24) + 1/6.37 x 10^6
=13690000 / 7.97732 x 10^13 + 1/6.37 x 10^6
1.716115187^-7 + 1.569858713^-7 = 3.2859739^-7
1/3.2859739^-7 = 3043237.806
then I do
3043237.806 - 6.37 x 10^6 but that gives me a negative height.
Can someone help me? I've been going at this problem for hours.
An object is projected upward from the surface of the Earth with an initial speed of 3.7 km/s. Find the maximum height it reaches.
m
Ive used the Energy conservation
Kf + Uf = Ki + Ui
1/2 mvf^2 - G*M_e*m/rf = 1/2 mvi^2 - G*M_e*m/ri
= 0 - G*M_e*m/rf = 1/2 mvi^2 - G*M_e*m/R_e
R_e = radius of Earth = 6.37 x 10^6m
M_e = mass of Earth = 5.98 x 10^24kg
G = 6.67 x 10^-11 N*m^2/kg^2
1/radius_f = -Vi^2/2*G*M_e + 1/R_e
1/radius_f = (-3700 m/s)^2 / 2(6.67 x 10^-11)(5.98 x 10^24) + 1/6.37 x 10^6
=13690000 / 7.97732 x 10^13 + 1/6.37 x 10^6
1.716115187^-7 + 1.569858713^-7 = 3.2859739^-7
1/3.2859739^-7 = 3043237.806
then I do
3043237.806 - 6.37 x 10^6 but that gives me a negative height.
Can someone help me? I've been going at this problem for hours.