Answer:
The correct answer to the following question will be "41.87 m".
Explanation:
The given values are:
The speed of trooper = 
The velocity of red car = 
Now,
A red car goes as far as possible until the speed or velocity of the troops is the same as that of of the red car at
(∵ 
)
then,
The distance covered by trooper,
The distance covered by red car,
= 
= 
Maximum distance = 
= 
Answer:
0.05 cm
Explanation:
The compression of the original spring = 12 - 8.55 cm = 3.45 cm = 0.0345 m
By Hooke's law, F = ke
Where F is the applied force, k is the spring constant and e is the extension or compression. In the question, F is the weight of the car.
k = F/e = 1355 × 9.8 / 0.0345 = 384898.55 N/m
This is the spring constant of the original spring. The question mentions that the force constant of the new spring is 5855.00 N/m smaller. Hence, the force constant of the new spring is 384898.55 - 5855 = 379043.55 N/m
With the new spring installed, the compression will be
e = F/k = 1355 × 9.8 / 379043.55 = 0.035 m = 3.5 cm
The difference in the compressions of both springs = 3.5 cm - 3.45 cm = 0.05 cm
The function y must be equal to 0 on any interval on which it is defined. The function y must be increasing (or equal to 0) on any interval on which it is defined.
Analysis of solution by seeing differential equation:
Given differential equation is: y' = (1/2)y2
How do deduce the results just by seeing them?
The equation tells us that:
rate = positive of ( y^2 )
rate = positive of (positive or zero) = positive or zero
Thus, the rate is positive or zero no matter what value we put in the place of y from its valid domain, since.
When the rate is positive or zero, that means the function will never grow upwards. Thus, either increasing or staying at the same level.
Learn more about differential equations here:
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<span>We can find the period P of one cycle, and then we can use the period to find the gravitational acceleration g on this planet.
P = (132 s) / (107 cycles) = 1.2336 s/cycle
The period P is 1.2336 seconds. This means that it takes 1.2336 seconds for the pendulum to swing back and forth one.
Now we can use the period P to find the gravitational acceleration g.
The equation for the period of a pendulum is as follows:
P = 2 pi \sqrt{L/g}
P^2 = (4 pi^2) L / g
g = (4 pi^2) L / P^2
g = (4)(pi^2)(0.540 m) / (1.2336 s)^2
g = 14.0 m/s^2
The acceleration of gravity on the planet is 14.0 m/s^2.</span>
