Question

Ball 1 and Ball 2 are initially at rest at ground level. At t = 0 Ball 1 is launched vertically upward with an initial speed V0. One second later Ball 2 is launched vertically upward with the same initial speed V0. Neither ball reaches its maximum height until several seconds after the second ball is launched.

1)

Ignoring any effects due to air resistance, which of the following statements best describes the distance between the balls after the second ball is launched but before the first ball reaches its maximum height?

The distance between the balls increases as they move upward.

The distance between the balls decreases as they move upward.

The distance between the balls stays the same as they move upward.

2)

Ignoring any effects due to air resistance, which of the following statements best describes the difference in speeds of the balls after the second ball is launched but before the first ball reaches its maximum height?

The difference in their speeds increases as they move upward.

The difference in their speeds decreases as they move upward.

The difference in their speeds stays the same as they move upward.

Answer 1

(1) Let us check the vertical distance between Ball-1 and Ball-2 when they move upward .

For Ball-1, h1 = u t - (1/2) g t2

For Ball-2, h2 = u (t-2) - (1/2) g (t-2)2

We get distance betwee balls from above equations = h1 - h2 = 2u + 2g [ 1 - t ]

As seen from above equation, distance between balls decreases with time

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(2)

Let us check the speed between Ball-1 and Ball-2 when they move upward .

For Ball-1, u1 = u - g t

For Ball-2, u2 = u - g (t-2)

We get speed difference betwee balls from above equations = -2g

As seen from above equation, difference between speeds remain same

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