Question

43 Человек массой 60 кг. бегуший со скоростью 8 км\ч. , догоняет тележку массой 80 кг. движущуюся со скоростью 2,9 км\ч , и вскакивает на неё. С какой скоростью бедет двигаться тележка?

Answer 1

СИ:

8км/ч=2.2м/с

2.9км/ч=0.8м/с

 

m1v1+m2v2=(m1+m2)v

v=m1v1+m2v2/(m1=m2)=60кг*2.2м/с+80кг*0.8м/с/(60кг+80кг)=

=132+64/140=1.4м/с

Answer 2

Problem Analysis

We have a person with a mass of 60 kg running at a speed of 8 km/h who catches up to a cart with a mass of 80 kg moving at a speed of 2.9 km/h and jumps onto it. We need to determine the speed at which the cart will be moving after the person jumps on.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the person jumps onto the cart is equal to the total momentum after the person jumps onto the cart.

The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum of the person before jumping onto the cart is given by:

Momentum of person before = mass of person * velocity of person

Similarly, the momentum of the cart before the person jumps onto it is given by:

Momentum of cart before = mass of cart * velocity of cart

After the person jumps onto the cart, the combined mass of the person and the cart will be the sum of their individual masses. Let's denote the final velocity of the combined system as V.

Using the principle of conservation of momentum, we can write the equation:

Momentum of person before + Momentum of cart before = Momentum of combined system after

Substituting the values, we have:

(mass of person * velocity of person) + (mass of cart * velocity of cart) = (mass of person + mass of cart) * V

Now we can solve this equation to find the final velocity of the cart.

Calculation

Let's substitute the given values into the equation and solve for V.

- Mass of person (m1) = 60 kg - Velocity of person (v1) = 8 km/h = 8/3.6 m/s (converted to m/s) - Mass of cart (m2) = 80 kg - Velocity of cart (v2) = 2.9 km/h = 2.9/3.6 m/s (converted to m/s)

Using the equation:

(m1 * v1) + (m2 * v2) = (m1 + m2) * V

Substituting the values:

(60 * (8/3.6)) + (80 * (2.9/3.6)) = (60 + 80) * V

Simplifying the equation:

(480/3.6) + (232/3.6) = 140 * V

133.33 + 64.44 = 140 * V

197.77 = 140 * V

Dividing both sides by 140:

V = 197.77 / 140

V ≈ 1.41 m/s

Therefore, the cart will be moving at a speed of approximately 1.41 m/s after the person jumps onto it.

Answer

The cart will be moving at a speed of approximately 1.41 m/s after the person jumps onto it.