After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.2 m/s. Miranda runs after her at a velocity of +4.5 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 57 kg, and Miranda's is 77 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.

vf = (m1 v1i + m2 v2i) / (m1 + m2) =

(57*2.2+77*4.5)/(57+77) =3.5 m/s

Well, it sounds like Ashley and Miranda are having a snow-tastic adventure! Let's find out how fast they slide together on the inner tube.

We know that Ashley's velocity is +2.2 m/s and Miranda's velocity is +4.5 m/s when she hops on the inner tube. To find their combined velocity, we can add up their individual velocities.

So, the combined velocity of Ashley and Miranda sliding on the inner tube is:

2.2 m/s + 4.5 m/s = 6.7 m/s

Ta-da! They're cruising at a cool 6.7 m/s across the snowfield. Just remember to steer clear of any funny-looking snowmen along the way!

To find the combined velocity of Ashley and Miranda sliding on the inner tube, we need to apply the principle of conservation of momentum.

The momentum of an object is given by the product of its mass and velocity. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, Ashley has a mass of 57 kg and a velocity of +2.2 m/s, so her momentum is given by:
Momentum of Ashley before = mass of Ashley × velocity of Ashley
= 57 kg × 2.2 m/s
= 125.4 kg·m/s

Miranda has a mass of 77 kg and a velocity of +4.5 m/s, so her momentum is given by:
Momentum of Miranda before = mass of Miranda × velocity of Miranda
= 77 kg × 4.5 m/s
= 346.5 kg·m/s

The total momentum before the collision is the sum of the individual momenta:
Total momentum before = Momentum of Ashley before + Momentum of Miranda before
= 125.4 kg·m/s + 346.5 kg·m/s
= 471.9 kg·m/s

After Miranda hops on the inner tube, they slide together. Let's assume their combined mass is the sum of their masses:
Combined mass = Mass of Ashley + Mass of Miranda
= 57 kg + 77 kg
= 134 kg

To find the combined velocity, we divide the total momentum before the collision by the combined mass:
Combined velocity = Total momentum before / Combined mass
= 471.9 kg·m/s / 134 kg
≈ 3.52 m/s

Therefore, the two of them will slide across the snow together on the inner tube at a speed of approximately 3.52 m/s.

To find the combined speed of Ashley and Miranda sliding on the inner tube, we need to use the concept of conservation of momentum. The momentum before they join should be equal to the momentum after they join.

Momentum is calculated as the product of mass and velocity. Therefore, the momentum of Ashley before Miranda joins is given by:

Momentum of Ashley = mass of Ashley × velocity of Ashley

= 57 kg × 2.2 m/s

= 125.4 kg·m/s

Similarly, the momentum of Miranda before joining is:

Momentum of Miranda = mass of Miranda × velocity of Miranda

= 77 kg × 4.5 m/s

= 346.5 kg·m/s

When they join on the inner tube, their momenta add together:

Total momentum after joining = Momentum of Ashley + Momentum of Miranda

= 125.4 kg·m/s + 346.5 kg·m/s

= 471.9 kg·m/s

Now, we can find the combined velocity of Ashley and Miranda on the inner tube by dividing the total momentum by the combined mass. The combined mass is the sum of their individual masses:

Combined mass = mass of Ashley + mass of Miranda

= 57 kg + 77 kg

= 134 kg

Combined velocity = Total momentum / Combined mass

= 471.9 kg·m/s / 134 kg

≈ 3.52 m/s

Therefore, the two of them slide across the snow together on the inner tube with a speed of approximately 3.52 m/s.