Final answer:
The final speed of the sled after a second 35-kg child jumps on is found using the conservation of momentum. The correct calculation gives a speed of 1.75 m/s, but as this is not a provided option, the closest value from the choices given is 2.0 m/s. There appears to be an error in the provided choices.
Step-by-step explanation:
The question asks for the speed of a sled after a second child jumps onto it. To find this, we can use the principle of conservation of momentum, which states that the total momentum before an event must equal the total momentum after the event if no external forces are acting on the system. The initial momentum of the system is the product of the mass of the first child and the velocity of the sled (35 kg × 3.5 m/s). When the second child jumps on the sled, the total mass of the children becomes 70 kg (35 kg + 35 kg). The final speed of the sled can be found by dividing the initial momentum by the new total mass:
Initial momentum = Mass1 × Velocityinitial = 35 kg * 3.5 m/s = 122.5 kg·m/s
Final speed = Initial momentum / Total mass = 122.5 kg·m/s / 70 kg = 1.75 m/s
However, looking at the provided multiple-choice answers, there seems to be an error as 1.75 m/s is not listed. If we select the closest value, the speed after the second child jumps on would be 2.0 m/s (option a), even though this is not the precise answer based on the calculation.