The initial velocity of the lead ball is 0 m/s. This is because it starts from rest and is only affected by the force of gravity.
Using the equation d = 1/2 * g * t^2, where d is the distance (5.00 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time, we can solve for t. It takes approximately 0.32 seconds for the lead ball to reach the water.
The impact velocity of the lead ball can be calculated using the equation v = g * t, where v is the velocity, g is the acceleration due to gravity, and t is the time. Plugging in the values, we get an impact velocity of approximately 3.14 m/s.
The lead ball will sink in the lake. This is because the density of lead is greater than that of water, causing it to sink to the bottom.
The depth of the lake will affect the impact of the lead ball. If the lake is deeper, the lead ball will have a longer distance to travel and therefore a higher impact velocity. However, factors such as the surface tension and temperature of the water may also play a role in the impact of the lead ball.