Set 4 Problem number 15

• Problem

• Solution 

• Generalized Solution

Problem

An object falls freely from rest for 1.24 seconds before striking the ground. Another object starts at the same time from the same location and travels horizontally at a constant 15 m/s.

• How far will the second object have traveled in the horizontal direction by the time the first object strikes the ground?
• How far will the first object travel in the vertical direction?

Solution

We can directly reason out the following results:

• In 1.24 seconds the horizontally moving object, traveling at 15 m/s, will travel ( 15 m/s)( 1.24 sec) = 18.6 m.

• The falling object will attain a vertical speed of (9.8 m/s/s)( 1.24 sec) = 12.152 m/s;
• its average speed will be (0+ 12.152 m/s)/2 = 6.076 m/s, and
• its will travel a vertical distance of ( 6.076 m/s)( 1.24 sec) = 7.53424 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.