a 25 kg boy on a 10 kg sled is coasting at 3.0 m/son level ice toward 30kg sister the girls jumps vertically and lands on her brothers back what is the final speed of the siblings and sled? neglect friction
final momentum = initial momentum
(25 + 10 + 30) v = (25+10) 3
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after an event remains the same if no external forces are acting.
Let's break down the problem step-by-step:
1. Calculate the initial momentum:
The initial momentum is the momentum of the boy and the sled before the jump. The formula for momentum is:
Momentum = Mass × Velocity
For the boy and the sled:
Initial Momentum = (Mass of Boy + Mass of Sled) × Velocity
Given values:
Mass of Boy (m1) = 25 kg
Mass of Sled (m2) = 10 kg
Velocity (v) = 3.0 m/s
Initial Momentum = (25 kg + 10 kg) × 3.0 m/s = 105 kg · m/s
2. Calculate the final momentum:
To find the final momentum after the girl jumps on her brother's back, we need to consider their combined mass. The final momentum is given by:
Final Momentum = Total Mass × Final Velocity
Total Mass = Mass of Boy + Mass of Sled + Mass of Sister
Total Mass = 25 kg + 10 kg + 30 kg = 65 kg
Given that the direction of the girl's jump is vertical, it will not affect the horizontal motion of the boy and sled. Therefore, the final velocity will be the same as the initial velocity.
Final Momentum = 65 kg × 3.0 m/s = 195 kg · m/s
3. Find the final velocity:
To calculate the final velocity, use the formula for momentum:
Final Momentum = Total Mass × Final Velocity
Rearrange the formula to solve for the final velocity:
Final Velocity = Final Momentum / Total Mass
Final Velocity = 195 kg · m/s / 65 kg = 3.0 m/s
Thus, the final speed of the siblings and sled, neglecting friction, is 3.0 m/s.