ching aing position of the steel ball are at the same height. (y; =Yf) The mass of the steel ball is 45 g, the initial speed of the ball is 3.85 m/s and the angle at which the ball is released is given as 55°. Mass of the steel ball expressed in SI units: Okg/s Okg*s Okg/m2 Okg Initial speed of ball is : Om*s/s Om/s Om/s? O1/m*s
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- Professional Application - (a) Calculate the maximum rate at which a rocket can expel gases if its acceleration cannot exceed seven times that of gravity. The mass of the rocket just as it runs out of fuel is 75,000-kg, and its exhaust velocity is 2.40x10 m/s. Assume that the acceleration of gravity is the same as on Earth’s surface (9.80 m/s2). (b) Why might it be necessary to limit the acceleration of a rocket?Antiballistic missiles (ABMs) are designed to have very large accelerations so that they may intercept fast-moving incoming missiles in the short time available. What is the takeoff acceleration (in m/s2) of a 10,000 kg ABM that expels 225 kg of gas per second at an exhaust velocity of 2.65 ✕ 103 m/s? (Enter the magnitude.)Two people are standing on a frictionless floor; person 1 (m1 = 150 kg) is on the right and pushes person 2 (m2 = 75 kg) standing on the left, with a 300N force over a distance of 1m after which they continue to slide away from each other; apply Newton’s 3rd and 2nd laws to calculate the velocity of each person when 5m apart:
- A baseball approaches home plate at a speed of 45.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 55.0 m/s straight up. The ball has a mass of 145g and is in contact with the bat for 2.00 ms. What is the average vector force the ball exerts on the bat during their interactions?Professional Application - One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100-mg chip of paint that strikes a spacecraft window at a relative speed of 4.00X10 m/s, given the collision lasts 6.00X10 s.Point masses of mass m1, m2, and m3 are placed at the points (-1, 0),(3, 0), and (0, 4).(a) Suppose that m 1 = 6. Find m2 such that the center of mass lies on they-axis.(b) Suppose that m1 = 6 and m2 = 4. Find the value of m3 such thaty = 2.
- Ball B is hanging from a cord of negligible weight. An identical ball A is measured 3m above the hanging ball and just touching the cord, is released from rest and acquires a velocity (V_o) before striking ball B. Assuming perfectly elastic impact and no friction, compute the A) magnitude of the velocity of ball A in terms of V_o or velocity before impact B.) direction of the velocity of ball A in terms of V_o or velocity before impact (note: should be in angle with respect to north, east, west, south)Two rods, with masses MA and MB having a coefficient of restitution, e, move along a common line on a surface, figure 2. a) Find the general expression for the velocities of the two rods after impact. b) IfmA =2kg,mB =1kg,vB=3m/s,ande=0.65,find the value of the initial velocity vA of rod A for it to be at rest after the impact and the final velocity v’B of rod B. c) Find the magnitude of the impulse for the condition in part b. d) Find the percent decrease in kinetic energy which corresponds to the impact in part b.A child in a boat throws a 5.50-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 26.6 kg and the mass of the boat is 36.4 kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest.Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the velocity is in the direction of the velocity of the box and negative value if the direction of the velocity is in the direction opposite to the velocity of the box.
- This is a two-part problem. A rocket, fired from rest at time t = 0, has an initial mass of m0 (including fuel). Assuming the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity v of the rocket will satisfy the equation m(dv/dt) = ck - mg. In this equation, g is the acceleration due to gravity. I) Find v(t) keeping in mind that the mass m is a function of t. II) Suppose that the fuel accounts for 70% of the initial mass of the rocket and that all of the fuel is consumed at 130 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted.A baseball approaches home plate at a speed of 45.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 55.0 m/s straight up. The ball has a mass of 145 g and is in contact with the bat for 2.00 ms. What is the average vector force the ball exerts on the bat during their interaction?Imagine a collision between two objects of equal mass traveling towards each other at the same speed. m1 = m2 and v2 = -v1. Which object will experience the largest force? Explain.