A freely body acquires a velocity of `g^(x)h^(y)` after falling through a height h. Using dimensions find the values fo x and y.

Explanation

To solve the problem of finding the values of \( x \) and \( y \) in the expression for velocity \( v = g^x h^y \) where \( g \) is the acceleration due to gravity and \( h \) is the height, we will use dimensional analysis.

### Step 1: Write down the dimensions of the quantities involved.
- The dimension of velocity \( v \) is \( [v] = L T^{-1} \).
- The dimension of acceleration due to gravity \( g \) is \( [g] = L T^{-2} \).
- The dimension of height \( h \) is \( [h] = L \).

### Step 2: Express the dimensions of the right-hand side.
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