Answer
After time t,
$Height = y_{0}-\frac{1}{2}gt^{2}$
On the other hand,
$t=\frac{x}{v_{0}cos\theta}$
Again, $(v_{0}sin\theta) t-\frac{1}{2}gt^{2}=xtan\theta-\frac{1}{2}gt^{2}=y_{0}-\frac{1}{2}gt^{2}$
Hence it is proved that at the time the bullet is in the path of the can, it is at same height as the can is.
Work Step by Step
After time t,
$Height = y_{0}-\frac{1}{2}gt^{2}$
On the other hand,
$t=\frac{x}{v_{0}cos\theta}$
Again, $(v_{0}sin\theta) t-\frac{1}{2}gt^{2}=xtan\theta-\frac{1}{2}gt^{2}=y_{0}-\frac{1}{2}gt^{2}$
Hence it is proved that at the time the bullet is in the path of the can, it is at same height as the can is.
