Two spheres, each of mass m, can slide freely on a...

Two spheres, each of mass $m,$ can slide freely on a frictionless, horizontal surface. Sphere $A$ is moving at a speed $v_{0}=16 \mathrm{ft} / \mathrm{s}$ when it strikes sphere $B,$ which is at rest, and the impact causes sphere $B$ to break into two pieces, each of mass $m / 2 .$ Knowing that 0.7 s after $B$ the collision one piece reaches point $C$ and 0.9 s a after the collision the other piece reaches point $D,$ determine $(a)$ the velocity of sphere $A$ after the collision, $(b)$ the angle $\theta$ and the speeds of the two pieces after the collision.

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00:01 Okay, so question a as for the velocity of spear a after collision.

00:09 So we will use the conservation of momentum equation to determine this.

00:15 So this is the equation.

00:31 Note that spear b is oppressed, so this is zero, and it breaks into two pieces.

00:42 So this is the final momentum.

00:43 Doom and was stated that sphere a and sphere b have equal mass, so it's denoted as m, while c and d also have equal mass that is equals to m over 2.

01:18 Then our equation becomes like this.

01:41 Then we can cancel this out and we're applying both sides of equation by 2, then we have this.

01:51 And this would be our expression to determine the speed of sphere a after collision.

02:20 So we have to determine the horizontal component of the two pieces, the horizontal component of the speed of the two pieces after collision, the two pieces form.

02:44 So we will use this equation.

02:48 We are given the time, you know, that for the velocity, it is equal to displacement over time.

02:55 The displacement is shown in the figure in the problem, which is 6 .3 feet.

03:09 And the time for c is 0 .7 seconds.

03:14 So this is 9 feet per second.

03:18 For d, we have the same displacement, but the time is different, which is 0 .9.

03:28 Then you can find that for the component of speed of this piece is 7 feet per second...

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