Answer:
Explanation:
Given
charge on alpha particle=+2e
mass of alpha particle=
kg
Charge on gold nucleus=+79e
Velocity at r=1m is 
Using Energy conservation
Kinetic energy of particle will be converting to Potential energy as it approaches to nucleus
therefore


![\frac{1}{2}\left ( 6.64\times 10^{-27}\right )\left ( 1.9\times 10^{7}^2\right )=\frac{9\times 10^9\times 158\times \left ( 1.6\times 10^{-19}\right )}{y}\left [\frac{1}{r_0}-\frac{1}{1}\right ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cleft%20%28%206.64%5Ctimes%2010%5E%7B-27%7D%5Cright%20%29%5Cleft%20%28%201.9%5Ctimes%2010%5E%7B7%7D%5E2%5Cright%20%29%3D%5Cfrac%7B9%5Ctimes%2010%5E9%5Ctimes%20158%5Ctimes%20%5Cleft%20%28%201.6%5Ctimes%2010%5E%7B-19%7D%5Cright%20%29%7D%7By%7D%5Cleft%20%5B%5Cfrac%7B1%7D%7Br_0%7D-%5Cfrac%7B1%7D%7B1%7D%5Cright%20%5D)
on solving we get


Answer:

Explanation:
It is assumed that pole vaulter began running at a height of zero. The physical model is formed after the Principle of Energy Conservation:


The previous expression is simplified and required height is found:

![h_{B} = \frac{1}{2 \cdot (9.807\, \frac{m}{s^{2}} )} \cdot [(10\, \frac{m}{s} )^{2}-(1.3\, \frac{m}{s} )^{2}]](https://tex.z-dn.net/?f=h_%7BB%7D%20%3D%20%5Cfrac%7B1%7D%7B2%20%5Ccdot%20%289.807%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%7D%20%5Ccdot%20%5B%2810%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D%20%29%5E%7B2%7D-%281.3%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D%20%29%5E%7B2%7D%5D)

Answer:
Metabolic power 420.138 W
Explanation:
Given data:
considering drag coefficient Cd = 0.9
Assuming cross section of cyclist A = 0.50 m^2
Take density of air ρ = 1.2 kg/m3
We know that drag force is given as


D = 14.388 N

hence metabolic power is given as
Metabolic power 

= 420.138 W
Answer:
t₁ > t₂
Explanation:
A coin is dropped in a lift. It takes time t₁ to reach the floor when lift is stationary. It takes time t₂ when lift is moving up with constant acceleration. Then t₁ > t₂, t₁ = t₂, t₁ >> t₂ , t₂ > t₁
Solution:
Newton's law of motion is given by:
s = ut + (1/2)gt²;
where s is the the distance covered, u is initial velocity, g is the acceleration due to gravity and t is the time taken.
u = 0 m/s, t₁ is the time to reach ground when the light is stationary and t₂ is the time to reach ground when the lift is moving with a constant acceleration a.
hence:
When stationary:

Hence t₂ < t₁, this means that t₁ > t₂.
The gravitational potential energy of an object of mass m at height h on earth is given by PEg=mgh