the 200 g baseball has a horizontal velocity of 30 m/s when it is struck by the bat, B, weighing 900 g, moving at 47 m/s. during the impact with the bat, how many impules of importance are used to find the final velocity of the bat

Solution :

Given :

Mass of the baseball, m = 200 g

Velocity of the baseball, u = -30 m/s

Mass of the baseball after struck by the bat, M = 900 g

Velocity of the baseball after struck by the bat, v = 47 m/s

According to the conservation of momentum,

(900 x 47) + (200 x -30)  = (900 x ) + (200 x )

36300 =  (900 x ) + (200 x )

..............(i)

The mathematical expression for the conservation of kinetic energy is

   ................(ii)

Substituting (i) in (ii)

Solving the equation, we get

The negative velocity is neglected.

Therefore, substituting 96 m/s for in (i), we get

     = 19

Thus, only impulse of importance is used to find final velocity.

Of course, with a triangle with a 90° angle, a right triangle, you can simply use pythagoras theorem  (a2+b2=c2)  then SOH-CAH-TOA to solve for the angle  (θ=Cos−1(adjacenthypotenuse)) .

But what if it isn't a right triangle? The cosine rule works for all triangles, even if they don't have a 90° angle.

a2=b2+c2−2(b)(c)Cos(A)  

Where a is the missing side, and A is the angle opposite to side a.

With this rule, we can find a missing angle or a missing side to any type of triangle, assuming you have the needed variables.

Explanation: