Physics, 31.07.2019 10:00 yahyaomf

2. a 200-kg boulder has 39,200 joules of gravitational potential energy. what height is it at? 3. a 1-kg model airplane has 12.5 joules of kinetic energy and 98 joules of gravitational potential energy. what is its speed? what is its height?

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We have that the gravitational energy is given by: U=mgh where m is the mass of the object (in kg), g is the gravitational acceleration and h is the height of the object (in meters). Hence, h=U/(m*g) where g=9.8 m/s^2. Thus, h=20 m if we substitute.
Similarly, substituting in b, we have that the height of the model plane is 10 m. The kinetic energy is given by: K= $\frac{1}{2} *m*u^2$ where u is the speed of the object. Hence, solving for u we have u= $\sqrt{2K/m}$ . Substituting, we have that u=5m/s.

Answer from: kmontello5

As per the first question we have to calculate the height at which the boulder is present.

we have been given the mass of the boulder [m] as 200 kg.

The gravitational potential energy is given as 39,000 Joule.

The gravitational potential energy at a height ' h' from the surface earth is given as P.E= mass×height×acceleration due to gravity

The value of g=9.8 m/s^2

Hence height [h] $=\frac{P.E}{mg}$

= $\frac{39000}{200*9.8} metre$

=19.8979 metre

As per the second question we have to calculate the sped and height of the model airplane.

the mass of model airplane is 1 kg

The kinetic energy [K.E] of the airplane is 12.5 joule

we have K.E $=\frac{1}{2} mass*speed^2$

K.E $=\frac{1}{2}mv^2$

$v^2=\frac{2K.E }{m}$

$v^2=\frac{2*12.5}{1}$

$v=\sqrt{25}$

v=5 m/s

Again we have to calculate the height [h]

The potential energy is given as 98 Joule.

we know that P.E= mgh

tex]h=\frac{P.E}{mg}[/tex]

= $\frac{98}{1*9.8} metre$

=10 metre

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

see earlier

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2. a 200-kg boulder has 39,200 joules of gravitational potential energy. what height is it at? 3. a...

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