<span>Answer:
So this involves right triangles. The height is always 100. Let the horizontal be x and the length of string be z.
So we have x2 + 1002 = z2. Now take its derivative in terms of time to get
2x(dx/dt) = 2z(dz/dt)
So at your specific moment z = 200, x = 100âš3 and dx/dt = +8
substituting, that makes dz/dt = 800âš3 / 200 or 4âš3.
Part 2
sin a = 100/z = 100 z-1 . Now take the derivative in terms of t to get
cos a (da./dt) = -100/ z2 (dz/dt)
So we know z = 200, which makes this a 30-60-90 triangle, therefore a=30 degrees or π/6 radians.
Substitute to get
cos (Ď€/6)(da/dt) = (-100/ 40000)(4âš3)
âš3 / 2 (da/dt) = -âš3 / 100
da/dt = -1/50 radians</span>
Answer:
Explanation:
The momentum of the first piece = m v =- m x 31 i kg m/s in - x direction direction
The momentum of the second piece = -m x 31 j kg m /s in Y - direction
Total momentum = - 31 m( i + j )
To conserve momentum , the third piece must have momentum equal to this
and opposite to it
So momentum of the third piece = 3m x V = 31 m ( i +j )
V = 31/3 ( i + j ) =
Magnitude of velocity V = √2 x 31/ 3 = 14.6 m / s
Its direction will be towards the vector i + j ie 45° from x - axis in positive direction
