Question

С тележки массой 210 кг, движущейся горизонтально со скоростью 3м/с, в противоположную сторону прыгает человек массой 70 кг. Какова скорость человека при прыжке, если скорость тележки стала равна 5м/с.

Answer 1

С тележки массой 210 кг, двидущейся горизонтально со скорость 2м/с в противоположную сторону прыгает человек массой 70 кг . Какова скорость человека при прыжке если скорость тележки стала 4 м/с.
V0=2м/с ; m1=210кг; V1=4м/с; m2=70кг ; V2-?;
(m1+m2)V0=m1V1 + m2V2
m2V2 = (m1+m2)V0 - m1V1
V2 =((m1+m2)V0 - m1V1) / m2
V2 = 280*2 - 210*4 / 70 = -280/70 = -4 м/с (скорость направлена в противоположную сторону)
ответ: а) 4 м/с

Answer 2

Calculation of the Person's Velocity

To calculate the velocity of the person when jumping off the cart, 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 is defined as the product of its mass and velocity. Let's denote the mass of the cart as M (210 kg) and the mass of the person as m (70 kg). The initial velocity of the cart is V1 (3 m/s), and the final velocity of the cart is V2 (5 m/s).

Using the conservation of momentum equation, we have:

(M * V1) + (m * 0) = (M + m) * V2 Since the person jumps off the cart, their final velocity is unknown, so we'll denote it as V.

Simplifying the equation, we get:

M * V1 = (M + m) * V2

Now, we can solve for V:

V = (M * V1) / (M + m)

Substituting the given values:

V = (210 kg * 3 m/s) / (210 kg + 70 kg)

Calculating the result:

V ≈ 1.714 m/s

Therefore, the velocity of the person when jumping off the cart is approximately 1.714 m/s.

Please note that this calculation assumes an idealized scenario without considering factors such as air resistance or the specific mechanics of the jump.