Physics, 14.09.2019 07:30 elijiahman99

If a body travels half it’s total path in the last 1.10s if it’s fall from rest, find the total time of its fall (in seconds)

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Answer from: sebastiantroysmith

3.75s

Explanation:

We can use the equations for constant acceleration motion. Let's call x, the total length of the path, then x/2 will be half of path. After falling from rest and reaching the half of its total path, the velocity of the body will be:

v_f^2 =v_0^2 + 2a(x/2)

vf is the final velocity, v0 is the initial velocity, 0m/s because the body starts from rest. a is the acceleration, gravity = 9.81m/s^2 in this case. Now, clearing vf we get:

$v_f=\sqrt{(0m/s)^2 + 2g(x/2)}\\v_f = \sqrt{g*x}In the second half:[tex]x/2 = \frac{1}{2}gtx^{2} + v_ot$

$x/2 = \frac{1}{2}g*(t)^2 + \sqrt{g*x}*(t)$

$(\frac{1}{2}\frac{(x-gt^2)}{\sqrt{g}t})^2 = x\\\\\frac{1}{4gt^2}(x^2 - 2xgt^2 + g^2t^4) = x\\\\\frac{1}{4gt^2}x^2 - (\frac{2gt^2}{4gt^2}+1)x + \frac{g^2t^4}{4gt^2} = 0\\ \frac{1}{4gt^2}x^2 - \frac{3}{2}x + \frac{gt^2}{4} = 0\\$

$0.0211 x^2 - 1.5x + 2.97 = 0\\$

Solving for x, you get that x is equal to 69.2 m or 2.03m. The total time of the fall would be:

$x = \frac{1}{2}gt^2\\t=\sqrt{(2x/g)}$

Trying both possible values of x:

$t_1 = 3.75 s\\t_2 = 0.64 s$

t2 is lower than 1.1s, therefore is not a real solution.

Therefore, the path traveled will be 69.2m and the total time 3.75s

Answer from: Quest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

Answer from: Quest

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

$_a^z\textrm{x}\rightarrow _{a-2}^{z-4}+_2^4\alpha$

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

$_a^z\textrm{x}+_{-1}^0\textrm{e}\rightarrow _{z-1}^a\textrm{y}$

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases $\gamma -radiations$ . this process does not change the mass number.

$_a^z\textrm{x}^*\rightarrow _a^z\textrm{x}+_0^0\gamma$

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as $\beta ^+$ -decay. in this the mass number remains same.

$_a^z\textrm{x}\rightarrow _{z-1}^a\textrm{y}+_{+1}^0e$

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

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If a body travels half it’s total path in the last 1.10s if it’s fall from rest, find the total time...

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