A 45 kg boy running at 3 meters per second jumps on to a 97 kg sled that is initially at rest. Find the resulting speed of the sled with the boy aboard.
To find the resulting speed of the sled with the boy aboard, we can use the principle of conservation of momentum. According to this principle, the total momentum before the jump is equal to the total momentum after the jump.
The momentum of an object can be calculated by multiplying its mass by its velocity (p = mv).
The mass (m) and velocity (v) of the boy are given as 45 kg and 3 m/s, respectively. We can calculate the momentum of the boy before the jump:
Momentum of the boy = mass of the boy × velocity of the boy
= 45 kg × 3 m/s
= 135 kg·m/s
Since the sled is initially at rest, its momentum is zero.
Total momentum before the jump = Momentum of the boy + Momentum of the sled
= 135 kg·m/s + 0 kg·m/s
= 135 kg·m/s
According to the principle of conservation of momentum, the total momentum after the jump should be equal to the total momentum before the jump.
The mass of the sled is given as 97 kg. Let's assume the resulting speed of the sled with the boy aboard is v (m/s).
Total momentum after the jump = (Mass of the boy + Mass of the sled) × Resulting speed of the sled with the boy aboard
= (45 kg + 97 kg) × v
= 142 kg × v
Equating the total momentum before the jump and after the jump, we have:
135 kg·m/s = 142 kg × v
Now, let's solve for v:
v = (135 kg·m/s) / (142 kg)
v ≈ 0.95 m/s
Therefore, the resulting speed of the sled with the boy aboard is approximately 0.95 m/s.
To find the resulting speed of the sled with the boy aboard, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the jump should be equal to the total momentum after the jump.
Let's denote the mass of the boy as m1 (45 kg) and the mass of the sled as m2 (97 kg). The initial velocity of the boy is v1 (3 m/s) and the initial velocity of the sled is v2 (0 m/s).
The total momentum before the jump can be calculated as:
Momentum before = (mass of the boy * initial velocity of the boy) + (mass of the sled * initial velocity of the sled)
= (m1 * v1) + (m2 * v2)
= (45 kg * 3 m/s) + (97 kg * 0 m/s)
= 135 kg*m/s
Since the sled is initially at rest (v2 = 0 m/s), the total momentum before the jump is simply the momentum of the boy.
Now, let's find the total momentum after the jump. After the boy jumps onto the sled, they move together as a single object. Let's denote their combined mass as M and the resulting velocity as v.
The total momentum after the jump can be calculated as:
Momentum after = Total mass after * Resulting velocity
= (m1 + m2) * v
Applying the principle of conservation of momentum, we can set the total momentum before the jump equal to the total momentum after the jump:
Momentum before = Momentum after
135 kg*m/s = (m1 + m2) * v
Rearranging the equation to solve for v:
v = 135 kg*m/s / (m1 + m2)
v = 135 kg*m/s / (45 kg + 97 kg)
v = 135 kg*m/s / 142 kg
v ≈ 0.95 m/s
Therefore, the resulting speed of the sled with the boy aboard is approximately 0.95 m/s.
Hint: linear momentum is conserved.
Mboy*(3 km/s) = (Mboy + Msled)*Vfinal