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- Mr.M is riding on his bike while pulling his daughter in a trailer behind him. Their combined mass is 125kg. He is riding at 44km/h [E] when he notices a red light 25m away. Assuming he breaks for a moment he sees the red light, what force would his breaks have to apply in order for him to be at rest when he gets to the light?A 3 kg mass is located at (-3, 3), a 7 kg mass is located at (4, 2) and a 1.2 kg mass is located at (1, -1). (a) Calculate the x coordinate and y coordinate of the center of mass for the mass system. (b) What happens to the center of mass as the 1.2 kg mass is gradually increased?You are abducted by aliens and find yourself locked in a large room on some strangeplanet. To pass the time, you decide to do some experiments using a ball-and-chain thatyou find on the floor. You make the following estimates:mBALL approximately equals 7 kg, mCHAIN approximately equals 0.5 kg, and CHAIN approximately equals 2 m. (a) When you hold the free end of the chain above your head and allow the ball to swinglike a pendulum, you use your wristwatch to measure the period as T approximately equals 4s. What is theacceleration due to gravity on this planet? Give explanation to your answer (b)If the ball accidentally hits a wall, how long does it take for this jolt in the chain totravel up to your hand?
- Two sumo wrestlers are in a match and at the start, they both lunge at each other. When they hit each other they miraculously come to a stand still. The first wrestler had a mass of 196 kg and was traveling at a velocity of 2.3 m/s at the instance of the collision. a) If the second wrestler was traveling at 2.7 m/s at the moment of the collision, what was his mass in kg?4. A rocket accelerates by burning its onboard fuel, so that its mass decreases with time.Suppose that the initial mass of the rocket at liftoff (including its fuel) is m, the fuel isconsumed at rate r, and the exhaust gases are ejected with constant velocity ν (relativeto the rocket). A model for the velocity of the rocket at time t is given by the equationv(t) = −ν ln(1 −Rt) −gt,where g is the acceleration due to gravity, R = r/m, and t is not too large.(a) Find an expression for the acceleration, a(t) = v′(t), of the rocket at any time t.(b) Find an expression for the position of the height, h(t), of the rocket at any timet. You can assume that at t = 0, the rocket hasn’t left the ground. Hint: re-member that ν,R,g are all constants and t is the independent variable.Write out your steps carefully!(c) Let g = 9.8 m/s2, R = 0.005 s−1. What does the velocity of the exhaust gases,ν, need to be for the rocket to reach a height of 6000 m one minute after liftoff?You can round to the…A 10kg mass, initally at rest, is dropped from a height of 15 meters above the horizontal. Determine the mass: a) original Pe; b) the mass velocity at impact; with the ground; and c) time to hit the ground.