a ball is shot from the ground straight up into the air with initial velocity of 50 50 ft/sec. assuming that the air resistance
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Answer:
, assuming that
and
are point charges.
Explanation:
Let denote the coulomb constant. Let
denote the distance between the two point charges. In this question, neither
and
depend on the value of
.
By Coulomb's Law, the magnitude of electrostatic force between and
would be:
.
Find the first and second derivative of with respect to
. (Note that
.)
First derivative:
.
Second derivative:
.
The value of the coulomb constant is greater than
. Thus, the value of the second derivative of
with respect to
would be negative for all real
.
would be convex over all
.
By the convexity of with respect to
, there would be a unique
that globally maximizes
. The first derivative of
with respect to
should be
for that particular
. In other words:
<em>.</em>
.
.
In other words, the force between the two point charges would be maximized when the charge is evenly split:
.
(a) The turtle's initial velocity is 4 m/s, initial position of the turtle is 5 cm, and initial acceleration is -1.25 m/s².
(b) The time when the velocity of the turtle is zero is 3.2 s.
(c) The time taken for the turtle to return to its starting point is 6.4 s.
(d) The time taken for the turtle to travel 30 cm is 0.08 s.
<h3>Initial velocity of the turtle</h3>The initial velocity of the turtle is calculated as follows;
The initial acceleration of the turtle is calculated as follows;
x(t) = 5 + 4t - 0.625t²
x(0) = 5 cm
<h3>Time when the velocity becomes zero</h3>v(t) = 4 - 1.25t
0 = 4 - 1.25t
1.25t = 4
t = 4/1.25
t = 3.2 s
<h3>Time taken to return to starting point</h3>The total distance traveled is calculated as follows
v² = u² + 2ad
0 = (4)² + 2(-1.25)d
0 = 16 - 2.5d
2.5d = 16
d = 16/2.5
d = 6.4 m
Time to travel the given distance;
d = ut + ¹/₂at²
6.4 = (4)t + ¹/₂(-1.25)t²
6.4 = 4t - 0.625t²
0.625t² - 4t + 6.4 = 0
solve the quadratic equation using formula method;
t = 3.2 s
The time travel the distance two times, = 2 x 3.2 s = 6.4 s
<h3>Time taken for the turtle to travel 30 cm</h3>d = ut + ¹/₂at²
0.3 = (4)t + ¹/₂(-1.25)t²
0.3 = 4t - 0.625t²
0.625t² - 4t + 0.3 = 0
solve the quadratic equation using formula method;
t = 0.08 s
Learn more about velocity here: brainly.com/question/6504879