Word Problem with Radicals

[vanbeersj]

The velocity 'v' of an object that falls through a distance 'h' is given by v = (2gh)^1/2, where g is the acceleration due to gravity. Two objects are dropped from heights that differ by 10.0 m such that the sum of their velocities when they strike the ground is 20.0 m/s. Find the heights from which they are dropped if g = 9.8 m/s^2.

For my equations I have:
H1=H2+10
V1+V2=20 which is V1=20-V2

If I take both H1 and V1 and substitue into the original equation I'm left with an equation that has still two variables of H and V and I'm not sure how to get it to the one variable to solve the problem.

 

[Deleted member 4993]

The velocity 'v' of an object that falls through a distance 'h' is given by v = (2gh)^1/2, where g is the acceleration due to gravity. Two objects are dropped from heights that differ by 10.0 m such that the sum of their velocities when they strike the ground is 20.0 m/s. Find the heights from which they are dropped if g = 9.8 m/s^2.

For my equations I have:
H1=H2+10
V1+V2=20 which is V1=20-V2

If I take both H1 and V1 and substitue into the original equation I'm left with an equation that has still two variables of H and V and I'm not sure how to get it to the one variable to solve the problem.

\(\displaystyle v_1 \, = \, \sqrt{2gh_1}\)

\(\displaystyle v_2 \, = \, \sqrt{2gh_2}\)

\(\displaystyle v_1 \, + \, v_2 \, = \, 20\)

\(\displaystyle h_1 \, - \, h_2 \, = \, 10\)

Four equations and four unknowns.

\(\displaystyle \sqrt{2gh_1} \, + \, \sqrt{2gh_2} \, = \, 20\)

\(\displaystyle \sqrt{2gh_1} \, + \, \sqrt{2g(h_1 \, - \, 10)} \, = \, 20\)

One equation - one unknown....