Question

At time t = 0 s, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. The figure gives the vertical positions y of the apples versus t during the falling, until both apples have hit the roadway. The scaling is set by ts = 2.0 s. With approximately what speed is apple 2 thrown down?

Answer 1

Concepts and reason

The concepts used to solve this problem are displacement and velocity with respect to time for falling objects.

First find the displacement of an apple 2 falls until reaches a ground by considering the displacement of apple 1 equal to the displacement of apple 2, because both the apples are thrown from the same height.

Finally find the speed of an apple 2 by calculating the time.

Fundamentals

The change in position of an object is called displacement. The change in position happens either horizontally or vertically.

The apple 1 is thrown from a bridge at $t=0s $. So, the initial velocity is zero.

The expression for the displacement of an apple 1 falls until reaches a ground is,

Here, is the final position, is the initial position, is the gravitational constant, and is the time.

Final position is zero so the equation is reduced to,

…… (1)

Again apple 2 is thrown from the same height with different time interval.

The expression for the displacement of an apple 2 falls until reaches a ground is,

Here is the speed of the apple 2.

Final position is zero. So, the expression for the speed of the apple 2 is,

…… (2)

The expression for the displacement of an apple 1 falls until reaches a ground is,

Apple 2 is also thrown from the same height.

Substitute for and for .

The expression for the speed of the apple 2 is,

From graph, the time taken to reach the apple 2 to the ground is,

Substitute for , for , and for in (2).

The negative sign represents that direction of an apple 2 is in downward.

Therefore, the speed of the apple 2 is .

Ans:

The speed of the apple 2 is .