I came across a question related to Brownian motion. May someone gives me a hint on this?
Suppose a leaf is falling from 1 metre(100 cm) above the ground. It is moving with Brownian motion vertically with volatility($\sigma^2$) $4cm^2/s$ and also has an average moving speed of 5cm/s vertically downward. What is the expectation of the leaf falls on the ground?
I am guessing one should model this as $$dX_t = 5dt + 2dB_t$$ where $B_t$ is a standard Brownian motion. And then, I am guessing to use the property that $Y_t^2-t$ is a martingale if $Y_t$ is a martingale. Hence, by setting $t$ to the stopping time that the leaf falls on the ground, we can deduce $E(t)$.
I am then guessing I should use a change of measure to transform $X_t$ to a martingale so I can apply my guessing above. Am I correct on this? Could someone guide me, please?