On a raft weighing 100 kg, having a speed of 1 m / s, directed along the river, a person weighing 50 kg

On a raft weighing 100 kg, having a speed of 1 m / s, directed along the river, a person weighing 50 kg jumps at a speed of 1.5 m / s perpendicular to the shore. What will be the overall speed of the raft and the person?

Given:

m1 = 100 kilograms is the mass of the raft;

v1 = 1 m / s (meter per second) – raft speed;

m2 = 50 kilograms – the mass of a person;

v2 = 1.5 m / s – human speed.

It is required to determine v (m / s) – the general speed of the raft and the person.

Since the speeds of the raft and the person are perpendicular to each other, we will find a common impulse after their interaction:

p = (p1 ^ 2 + p2 ^ 2) ^ 0.5;

p = ((100 * 1) ^ 2 + (50 * 1.5) ^ 2) ^ 0.5;

p = (100 ^ 2 + 75 ^ 2) ^ 0.5;

p = (10000 + 5625) ^ 0.5 = 15625 ^ 0.5 = 125 kg * m / s.

Then the speed of the raft and the person will be equal to:

v = p / M = 125 / (100 + 50) = 125/150 = 0.8 m / s (the result has been rounded to one decimal place).

Answer: the total speed of the raft and the person will be 0.8 m / s.