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# Solid mechanics with a positive reference

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1. A 2-lb ball is thrown upward at 30ft/s from an origin 5-ft above the earth's surface. Using for your positive reference a vertical Y axis with its origin at 5ft, DETERMINE FOR THE BALL:

a) The maximum height in ft reached
b) The elapsed time of flight in seconds until its return to the origin
c) Its acceleration in ft/s2 at the highest point
d) Its velocity vector at its return to the origin

2. The velocity of a 0.1kg particle along a horizontal X axis is given by:
v(t)=(8t2 -20)m/s, and at t=20s, v(20)=60m. DETERMINE FOR t=8s:

a) The position of the particle in ft
b) The velocity of the particle in ft/s
c) The acceleration of the particle in ft/s2

3. The acceleration of an object in rectilinear x-direction motion is given by:
a(v)=0.4-0.0002v2 ft/s. If v=0 when x=0. DETERMINE FOR THE OBJECT:

e) Its velocity in ft/s when x=1000ft
f) Its acceleration in ft/s2 at x=1000ft
g) Its maximum velocity in ft/s

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https://brainmass.com/physics/velocity/solid-mechanics-positive-reference-161165

#### Solution Preview

Please see the attached file.

The velocity , where s is the displacement of the object,
And the acceleration

On the other hand, we have
The velocity is
The displacement

1. A 2-lb ball is thrown upward at 30ft/s from an origin 5-ft above the earth's surface. Using for your positive reference a vertical Y axis with its origin at 5ft, DETERMINE FOR THE BALL:

a) The maximum height in ft reached
b) The elapsed time of flight in seconds until its return to the origin
c) Its acceleration in ft/s2 at the highest point
d) Its velocity vector at its return to the origin

The ball is subject to the gravitational acceleration g all the time.
When the positive direction is upward, the acceleration a of the ball is
a = - g = - 32 ft/s2.

So the velocity is
, where c1 is the ...

#### Solution Summary

This shows how to solve a variety of velocity and position problems.

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