Set 4 Problem number 15

• Problem

• Solution 

• Generalized Solution

Problem

At a certain instant an object is released from rest into free fall, and a second object is struck, giving it a speed of 9 meters/second in the horizontal direction. The second object travels along the ground in a straight horizontal line at this constant speed.

• After precisely 1.72 seconds, the first object strikes the ground, and the second object strikes the first.
• How far did the second object move in the horizontal direction?

Solution

We can directly reason out the following results:

• In 1.72 seconds the horizontally moving object, traveling at 9 m/s, will travel ( 9 m/s)( 1.72 sec) = 15.48 m.

• The falling object will attain a vertical speed of (9.8 m/s/s)( 1.72 sec) = 16.856 m/s;
• its average speed will be (0+ 16.856 m/s)/2 = 8.427999 m/s, and
• its will travel a vertical distance of ( 8.427999 m/s)( 1.72 sec) = 14.49616 m.

Generalized Solution

In `dt seconds an object traveling in the horizontal direction at constant velocity vx will travel through a displacement of

• `dsx = vx * `dt.

In the same time an object falling freely from rest will have initial velocity v0y = 0 and acceleration ay = g (the acceleration of gravity).  It will therefore travel through a displacement of

• `dsy = v0y * `dt + .5 ay `dt^2 = .5 g `dt^2.