Question

A 50.0 kg boy runs at a speed of 10.0 m/s and jumps onto a cart. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

A) 150 kg
B) 175 kg
C) 210 kg
D) 260 kg
E) 300 kg

Answer 1

Using the conservation of momentum, the mass of the cart is calculated to be 150 kg when a 50.0 kg boy running at 10.0 m/s jumps onto it, and they move together at a velocity of 2.50 m/s.

Step-by-step explanation:

The subject of this question is Physics, specifically it relates to the conservation of momentum. To find the mass of the cart, we can use the principle of conservation of momentum, which states that the total momentum before an event must equal the total momentum after, provided no external forces act on the system. The equation for conservation of momentum is m1 * v1 + m2 * v2 = (m1 + m2) * v' where m1 is the mass of the boy, v1 is the velocity of the boy, m2 is the mass of the cart (which we need to find), v2 is the velocity of the cart before the boy jumps on it, and v' is the final velocity of the combined system.

Before the boy jumps onto the cart, the cart's initial velocity, v2, is 0 m/s, and the final combined velocity after the boy jumps on is given as 2.50 m/s. Using these values:

(50.0 kg * 10.0 m/s) + (m2 * 0 m/s) = (50.0 kg + m2) * 2.50 m/s.

Solving for m2 gives:

500 kg*m/s = (50.0 kg + m2) * 2.50 m/s

500 kg*m/s = 125 kg*m/s + 2.50 m/s * m2

500 kg*m/s - 125 kg*m/s = 2.50 m/s * m2

375 kg*m/s = 2.50 m/s * m2

m2 = 375 kg*m/s / 2.50 m/s

m2 = 150 kg

The mass of the cart is therefore 150 kg, which corresponds to answer choice (A).