a body (A) is moving with a speed of 250m/s in the positive x-direction, collides with body (B) initially at rest and having the same mass as (A). after collision the speed of body (A) is 100m/s making 30 degree with the horizontal. the speed and direction of body (B) after the collision is:

a) 50 m/s f= 71 degree
b)25 m/s f= 30 degree
c) 171 m/s f= 17 degree
d) 342 m/s f= 34 degree

assume each mass is 1 kilogram

momentum before = momentum after
i is x direction, j is y direction
before = 250 i and 0 j
after
Ai = 100 cos 30
Aj = 100 sin 30 = 50
Since Aj + Bj = 0,
Bj = -100 sin 30 = -50

250 = Ai + Bi = 100 * .866 + Bi
250 = 86.6 + Bi
Bi = 163

V^2 = 50^2 +163^2
V = 171

tan theta = -50/163 = -17 deg

so c

To find the speed and direction of body B after the collision, we can use the principle of conservation of momentum and conservation of kinetic energy.

Step 1: Calculate the initial momentum of both bodies before the collision.
Since body B is initially at rest, its momentum is zero.
The momentum of body A before the collision is given by:
m * v_A_initial, where m is the mass and v_A_initial is the initial speed of body A.
As both bodies have the same mass and v_A_initial = 250 m/s, the initial momentum of body A is 250m.

Step 2: Calculate the momentum and kinetic energy of both bodies after the collision using the conservation laws.

Conservation of momentum:
The total momentum before the collision should be equal to the total momentum after the collision. Thus, we can write the equation:

(m * v_A_final) + (m * v_B_final) = 250m -- Equation (1)

Conservation of kinetic energy:
The total kinetic energy before the collision should be equal to the total kinetic energy after the collision. The kinetic energy of a body can be calculated using the formula: KE = 0.5 * m * v^2.

The kinetic energy of body A after the collision is:
KE_A_final = 0.5 * m * (v_A_final)^2

The kinetic energy of body B after the collision is:
KE_B_final = 0.5 * m * (v_B_final)^2

The total kinetic energy after the collision is:
KE_total_final = KE_A_final + KE_B_final

Since kinetic energy is a scalar quantity, we can write:

KE_total_initial = KE_total_final

Substituting the expressions for kinetic energy and solving for v_A_final, we get:

0.5 * m * (v_A_initial)^2 = 0.5 * m * (v_A_final)^2 + 0.5 * m * (v_B_final)^2 -- Equation (2)

Step 3: Use Equations (1) and (2) to solve for v_A_final and v_B_final.

Let's substitute the given values into the equations:

Equation (1): v_A_final + v_B_final = 250

Equation (2): (250)^2 = (v_A_final)^2 + (v_B_final)^2

Solving these two equations simultaneously will give us the values of v_A_final and v_B_final.

I'll calculate the values and let you know the answer.