The velocity of a freely falling body changes as gphq where g is acceleration due to gravity and h is the height. The values of p and q are

v ∝ gphqgivenBy substituting the dimension of each quantity and comparing the powers in both sides we get LT−1 = LT-2PLq⇒ p+q = 1,  −2p = −1, ∴ p =12, q = 12