3.4** Two hobos, each of mass mɲ, are standing at one end of a stationary railroad flatcar with frictionless wheels and mass mfc. Either hobo can run to the other end of the flatcar and jump off with the same speed u (relative to the car). (a) Use conservation of momentum to find the speed of the recoiling car if the two men run and jump simultaneously. (b) What is it if the second man starts running only after the first has already jumped? Which procedure gives the greater speed to the car? [Hint: The speed u is the speed of either hobo, relative to the car just after he has jumped; it has the same value for either man and is the same in parts (a) and (b).]

Suppose an object of mass m, initially travelling with a velocity v1, collides with an object of mass m initially at rest. Prove that the angle between the velocity vectors of the two objects of the two particles after the collision is 90 degrees.

Vahé and Nicolás, both with mass M, are playing catch with a football of mass m on the frictionless surface of a frozen pond. Since they're physics professors and not professional football players, they can only throw the football with a speed vo be only in terms of m, M, and vo- relative to themselves. All of your answers below should (а) Relative to a stationary observer on the surface of the pond, what is the speed v, with which the football is moving after it is Vahé throws the ball to his right, toward Nicolás. m M V |NM thrown? (b) Nicolás catches the ball. What is the speed v, with which Nicolás and the ball are moving after he catches the ball?

As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed  (0.516)v  after passing through the target. The collision is inelastic and during the collision, the amount of kinetic energy lost by the bullet and paper is equal to [(0.333)Kb BC] , that is, 0.333 of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V =____v M = ___m

The mass of a particular skateboard plus its rider is ms=78.6kg, and the skateboarder is holding a book with mass mb=3.07kg. Initially at rest, the skateboarder tosses the textbook with a velocity of vb=2.74m/s at an angle θ=24.3∘ above the horizontal, and the book is caught by a friend. Calculate the magnitude, in meters per second, of the velocity of the student. What is the magnitude, in newton seconds, of the momentum, pE, which was transferred to the the Earth during the time the book was being thrown?

Consider a collision between two particles p and q in 3-D space R³. Suppose that the mass of p is a > 0 kilograms and the mass of q is b> 0 kg. i Let ; and 7; € R³ be the constant initial velocities of p and q, respec- tively. Let 7 and 7ƒ € R³ be the constant (final) velocities of p and q, respectively, after the collision; and assume ƒ ‡ ₁. (1) Write down an equation describing the physical fact that the total momentum of the particles p and q after the collision is equal to the the total momentum of p and q before the collision. 9 (2) The impulse of p associated with the change in velocity of p is given by 7 := a (Tƒ – Ui) · The analogous impulse of q is F := b (V ƒ – Vi) · 7 and 7 f Using Part (1), prove that the vectors (3) Assume further that the collision between p and q is elastic. So, the total kinetic energy of the particles p and q after the collision is equal to the the total kinetic energy of p and q before the collision. Write down an equation that precisely describes…

Question 2