Question

Four balls with different masses are dropped from the heights shown. Air resistance may be ignored. Which ball has the greatest average speed?

Answer 1

Answer:

The one falling from the greatest height will have the greatest speed.

h = 1/2 g t^2        time for ball to fall distance h

h2 / h1 = t2^2 / t1^2       dividing equations

h2 / t2^2 = h1 / t1^2

Let v be the average speed (v2 = h2 / t2)

1 / t2 * v2 = 1 / t1 * v1

v2 / v1 = t2 / t1      the one taking the longest to fall has the greater av. speed

Check:

h4 / h1 = t4^2 / t1^2     or

t4 / t1 = (h4 / h1)^1/2

In this case t4 / t1 = (4 / 1)^1/2 = 2  or twice the average speed

t1 = (2 h / g)^1/2 = .2^1/2 = .447       using g = 10

t4 = (2 h / g)^1/2 = .8^1/2 = .894

v1 = 1 / .447 = 2.24 m/s average speed

v4 = 4 / .894 = 4.47    or twice the average speed