<span>vf^2 = vi^2 + 2*a*d
---
vf = velocity final
vi = velocity initial
a = acceleration
d = distance
---
since the airplane is decelerating to zero, vf = 0
---
0 = 55*55 + 2*(-2.5)*d
d = (-55*55)/(2*(-2.5))
d = 605 meters
</span>
        
             
        
        
        
<h2>
Option 2 is the correct answer.</h2>
Explanation:
Elastic collision means kinetic energy and momentum are conserved.
Let the mass of object be m and M.
Initial velocity object 1 be u₁,  object 2 be u₂
Final velocity object 1 be v₁,  object 2 be v₂
Initial momentum = m x u₁ + M x u₂ = 3 x 8 + M x 0 = 24 kgm/s
Final momentum = m x v₁ + M x v₂ = 3 x v₁ + M x 6 = 3v₁ + 6M 
Initial kinetic energy = 0.5 m x u₁² + 0.5 M x u₂² = 0.5 x 3 x 8² + 0.5 x M x 0² = 96 J
Final kinetic energy = 0.5 m x v₁² + 0.5 M x v₂² = 0.5 x 3 x v₁² + 0.5 x M x 6² = 1.5 v₁² + 18 M
We have
             Initial momentum = Final momentum
             24 = 3v₁ + 6M 
             v₁ + 2M = 8
              v₁ = 8 - 2M
             Initial kinetic energy = Final kinetic energy
             96 = 1.5 v₁² + 18 M
             v₁² + 12 M = 64
Substituting  v₁ = 8 - 2M
            (8 - 2M)² + 12 M = 64    
            64 - 32M + 4M² + 12 M = 64    
             4M² = 20 M
                M = 5 kg
Option 2 is the correct answer.   
 
        
        
        
Answer:

Explanation:
Consider two particles are initially at rest. 
Therefore, 
the kinetic energy of the particles is zero.
That initial K.E. = 0
The relative velocity with which both the particles are approaching each other is Δv and their reduced masses are

now, since both the masses have mass m 
therefore, 

= m/2
The final K.E. of the particles is 

Distance between two particles is d and the gravitational potential energy between them is given by 

By law of conservation of energy we have 

Now plugging the values we get 



This the required relation between G,m and d 
 
        
             
        
        
        
Answer:
Explanation:
The cross product of two vectors is given by 

Where, θ be the angle between the two vectors and \widehat{n} be the unit vector along the direction of cross product of two vectors. 
Here, K x i = - j 
As K is the unit vector along Z axis, i is the unit vector along X axis and j be the unit vector along  axis. 
The direction of cross product of two vectors is given by the right hand palm rule. 
So, k x i = j 
j x i = - k 
- j x k = - i 
i x i = 0