A 63-kg ice-skater glides with a speed of 10 m/s toward a 14-kg sled at rest on the ice. The ice-skater reaches the sled and holds on to it. The ice-skater and the sled then continue sliding in the same direction in which the ice-skater was originally skating. What is the speed of the ice-skater and the sled after they collide?

conservation of momentum applies

momentumbefore=momentum after
63*10=(63+14)V

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The equation for momentum is:
Momentum = mass × velocity

Let's denote the initial speed of the ice-skater as "v1" and the speed of the sled after the collision as "v2".

Given:
Mass of the ice-skater (m1) = 63 kg
Speed of the ice-skater before the collision (v1) = 10 m/s
Mass of the sled (m2) = 14 kg
Speed of the sled before the collision (0 m/s, as it's at rest)

The total momentum before the collision is:
(m1 × v1) + (m2 × 0)
= (63 kg × 10 m/s) + (14 kg × 0)
= 630 kg m/s + 0 kg m/s
= 630 kg m/s

The total momentum after the collision is:
(m1 + m2) × v2, as the ice-skater and the sled move together after the collision.

Using the conservation of momentum principle, we have:
(m1 × v1) + (m2 × 0) = (m1 + m2) × v2

Substituting the given values, we get:
(63 kg × 10 m/s) + (14 kg × 0) = (63 kg + 14 kg) × v2

Simplifying the equation:
630 kg m/s = 77 kg × v2

Dividing both sides of the equation by 77 kg:
v2 = 630 kg m/s / 77 kg
v2 ≈ 8.18 m/s

Therefore, the speed of the ice-skater and the sled after they collide is approximately 8.18 m/s.

To find the speed of the ice-skater and the sled after they collide, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The equation for momentum is given by:

momentum = mass × velocity

Let's denote the initial velocity of the ice-skater as v1 and the final velocity of the ice-skater and the sled after the collision as v2.

Before the collision, the ice-skater is moving with a speed of 10 m/s towards the sled, and the sled is at rest. Therefore, their initial momenta are:

Ice-skater's initial momentum = mass of ice-skater × initial velocity of ice-skater
= 63 kg × 10 m/s

Sled's initial momentum = mass of sled × initial velocity of sled
= 14 kg × 0 m/s (as the sled is at rest)

The total initial momentum is the sum of the individual momenta:

Total initial momentum = Ice-skater's initial momentum + Sled's initial momentum

After the collision, the ice-skater and the sled slide together with the same final velocity, v2.

Therefore, the total final momentum is:

Total final momentum = (mass of ice-skater + mass of sled) × final velocity

Since the total momentum before the collision is equal to the total momentum after the collision, we can set up the equation:

Total initial momentum = Total final momentum

63 kg × 10 m/s = (63 kg + 14 kg) × v2

Now, we can solve for v2 to find the final velocity:

(63 kg × 10 m/s) / (63 kg + 14 kg) = v2

v2 ≈ 8.42 m/s

Therefore, the speed of the ice-skater and the sled after they collide is approximately 8.42 m/s.