Physics, 01.10.2019 04:00 katarawho

Alead ball is dropped in a lake from a diving board 5.20 m above the water. it hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. it reaches the bottom 4.80 s after it is dropped. (a) how deep is the lake? what are the (b) magnitude and (c) direction (up or down) of the average velocity of the ball for the entire fall? suppose that all the water is drained from the lake. the ball is now thrown from the diving board so that it again reaches the bottom in 4.80 s. what are the (d) magnitude and (e) direction of the initial velocity of the ball?

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Answer from: carterh166

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

Here, downward direction is considered positive

$v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 5.2+0^2}\\\Rightarrow v=10.1\ m/s$

$v=u+at\\\Rightarrow 10.1=0+9.81t\\\Rightarrow t=\frac{10.1}{9.81}=1.03\ s$

Time taken by the ball to reach the water is 1.03 seconds

Time in the water = 4.8 - 1.03 = 3.77 seconds

Distance = Speed × Time

⇒Distance = 10.1×3.77 = 38.077 m.

The lake is 38.077 m deep

Total distance the ball traveled is 5.2+38.077 = 43.277 m

Average velocity

$v_{avg}=\frac{43.277}{4.8}=9.02\ m/s$

Average velocity = 9.02 m/s Downward

Now, s = 43.277 m

t = 4.8 seconds

$s=ut+\frac{1}{2}at^2\\\Rightarrow u=\frac{s-\frac{1}{2}at^2}{t}\\\Rightarrow u=\frac{43.77-\frac{1}{2}\times 9.81\times 4.8^2}{4.8}\\\Rightarrow u=-14.42525\ m/s\ upward\ or\ 14.42525\ downward$

Here, the negative sign indicates that the ball would be thrown up with a velocity of 14.42525 m/s. When this ball will reach the height of the diving board it will gain the same speed as the initial upward velocity but the direction would change making it positive.

The ball could be thrown directly with a velocity of 14.42525 m/s which would make the sign positive.

Answer from: Quest

568.98

explanation:

its math

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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Alead ball is dropped in a lake from a diving board 5.20 m above the water. it hits the water with a...