By raising the ball to a ht. of ho, you give it a potential energy change of mg(ho), which will be converted to Kinetic energy when the ball comes down
mgho = 1/2m(v1^2), thus u get v1.
Find final velocities. use potential energy again after that.
Potential energy in above problem is essentially gravitational energy..(you can neglect other forms they don't play much of a role here)..and anyway there is NO CHANGE in gravitational energy if the bullet went horizantally through, right?? as h is same for both initial and final situation. So...
You r averaging the speed for individual laps.. (150 + v)/2 = 180, and thus v=210
Actually avg. speed = total distance/total time = (150*2d + v*2d)/[2d/150 + 2d/v] = 180
In short you r assuming that he takes equal time to complete the first 2 laps and the last 2 laps, which is incorrect.