Question

1. You are standing on top of the empire state building (334.87 m) when Superman flies past.  He is headed straight down with a steady speed of 20 m/s.  At the instant he goes past, you drop a 10 kg lead ball over the edge.  At what height does the ball catch up to Superman?

Answer 1

Irrespective of mass a freely falling object travels with a velocity of gt where g is acceleration due to gravity and t is time in seconds

The 10kg lead ball acquires a velocity of 20m/s in 2 sec

Distance travelled s = ut +(1/2) *g*t^2 for lead ball

Where as super man travelled with uniform velocity

Distance = 20*t

Equating both 1&2 , we get 5t^2 -20t = 0

5t(t-4) = 0; t =4;

After t = 4 seconds both objects meet

After travelling 80 meters from top of building both Superman and lead ball meet.

At 334.87 meters of building we have to subtract 80 indicates the height from ground where two objects meet is 254.87