A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up travelling at 1.6 m/s.

sin(30) = sin(a)

(.5)(1.6) (1.2)(.5)

sin(30)(.6) = sin(a)(.8)
sin(a)= (sin(30)(.6))/.8
sin(a)= .375
a= 22.024º

Therefore, b= equals:
180º- 22.024º- 30º = 127.976

sin(30) = sin(127.976)
(.5)(1.6) (.5)(v)

sin(30)(.5)(v) = sin(127.976)(.5)(1.6)
v = (sin(127.976)(.5)(1.6))/ (sin(30)(.5))
v= .6306148577 / .25
v= 2.522m/s

The cue ball original speed is 2.5 m/s.

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up travelling at 1.6 m/s.

physics - bobpursley, Wednesday, June 4, 2014 at 10:47pm

I think you can safely assume conservation of energy.

1/2 .5 V^2=1/2 .5 1.2^2 + 1/2 .5 1.6^2
solve for V

Well, now we're getting into some Newtonian fun! Let's get this ball rolling, shall we?

First, let's calculate the velocity of the billiard ball after the collision. Since it starts stationary and ends up traveling at 1.6 m/s, we know its velocity change is Δv = 1.6 m/s.

Now let's tackle the cue ball. We know it's initially moving with a certain speed, let's call it v, and ends up deflecting at a 30.0° angle with a speed of 1.2 m/s. Since we have some angles involved, we need to break the velocity down into its horizontal and vertical components.

The horizontal component of the initial velocity remains the same after the collision, but the vertical component becomes zero. This is because the glancing blow doesn't affect the horizontal motion of the cue ball but stops its vertical motion.

Using some trigonometry, we can determine the horizontal component of the velocity after the collision. It's given by v horizontal = v * cos(30.0°).

Since the cue ball deflects with a speed of 1.2 m/s after the collision, we can write the following equation:

v horizontal = 1.2 m/s

Now we can solve for the initial velocity, v:

v = 1.2 m/s / cos(30.0°)

Plug in those numbers into your trusty calculator, and you'll find the answer!

And remember, when life gets confusing, just imagine a clown juggling cue balls while riding a unicycle. It won't solve your physics problems, but it's definitely more entertaining!

To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.

Let's assume the initial speed of the cue ball is v1 (the magnitude of the velocity vector) and the initial speed of the billiard ball is v2 (the magnitude of the velocity vector).

Before the collision, the momentum of the system is given by:
p_initial = (mass of the cue ball * velocity of the cue ball) + (mass of the billiard ball * velocity of the billiard ball)
= (0.50 kg * v1) + (0.50 kg * 0) (since the billiard ball is stationary)

After the collision, the momentum of the system is given by:
p_final = (mass of the cue ball * final velocity of the cue ball) + (mass of the billiard ball * final velocity of the billiard ball)
= (0.50 kg * 1.2 m/s) + (0.50 kg * 1.6 m/s)

Since momentum is conserved, we can set the initial momentum equal to the final momentum and solve for v1.
(0.50 kg * v1) + (0.50 kg * 0) = (0.50 kg * 1.2 m/s) + (0.50 kg * 1.6 m/s)

Simplifying the equation:
0.50 kg * v1 = 0.50 kg * (1.2 m/s + 1.6 m/s)
v1 = (1.2 m/s + 1.6 m/s) / 0.50 kg

Calculating the value:
v1 = 3.8 m/s

Therefore, the original speed of the cue ball is 3.8 m/s.

To solve this problem, we can use the principles of conservation of momentum and the law of conservation of kinetic energy.

First, we can calculate the momentum of the billiard ball after the collision using the equation:

momentum = mass * velocity

Given that the mass of the billiard ball is 0.50 kg and its velocity after the collision is 1.6 m/s, we can calculate its momentum:

momentum of billiard ball = 0.50 kg * 1.6 m/s = 0.80 kg·m/s

Now, let's consider the cue ball. After the collision, it deflects at an angle of 30.0° from its original path and has a speed of 1.2 m/s. We need to calculate its velocity components in the x and y directions.

Given the speed, we can determine the x-component of the cue ball's velocity using the equation:

velocity_x = speed * cos(angle)

velocity_x = 1.2 m/s * cos(30.0°) = 1.2 m/s * √(3)/2 ≈ 1.04 m/s

Similarly, we can determine the y-component of the cue ball's velocity using the equation:

velocity_y = speed * sin(angle)

velocity_y = 1.2 m/s * sin(30.0°) = 1.2 m/s * 1/2 = 0.60 m/s

Next, we can calculate the momentum of the cue ball after the collision using the x and y components of its velocity:

momentum of cue ball = mass * velocity = 0.50 kg * √(velocity_x^2 + velocity_y^2)

momentum of cue ball = 0.50 kg * √(1.04^2 + 0.60^2) ≈ 0.50 kg * 1.21 ≈ 0.61 kg·m/s

Now, using the principle of conservation of momentum, we know that the total momentum before the collision is equal to the total momentum after the collision. Therefore, the sum of the momenta of the cue ball and the billiard ball after the collision is equal to the momentum of the billiard ball before the collision:

momentum of billiard ball before collision = momentum of cue ball + momentum of billiard ball

0.80 kg·m/s = 0.61 kg·m/s + momentum of billiard ball

Solving for the momentum of the billiard ball before the collision:

momentum of billiard ball before collision = 0.80 kg·m/s - 0.61 kg·m/s = 0.19 kg·m/s

Finally, we can find the original velocity of the cue ball using the equation for momentum:

momentum = mass * velocity

0.19 kg·m/s = 0.50 kg * velocity

Solving for the velocity:

velocity = 0.19 kg·m/s / 0.50 kg ≈ 0.38 m/s

Therefore, the original speed of the cue ball was approximately 0.38 m/s.