A certain ball has the property that each time it falls from a height $h$ onto a hard, level surface, it rebounds to a height$r h,$ where $0<r<1 .$ Suppose that the ball is dropped from an initial height of $H$ meters.(a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels.(b) Calculate the total time that the ball travels. (Use the fact that the ball falls $\frac{1}{2} g t^{2}$ meters in $t$ seconds.(c) Suppose that each time the ball strikes the surface with velocity $v$ it rebounds with velocity $-k v,$ where $0<k<1 .$ How long will it take for the ball to come to rest?

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6. Suppose an object is thrown up in the air and then it falls back down. Its height is given by the function S h(t) = 20t2 (2 – t). (a) Find the velocity function. (b) At what time t > 0 does the object hit the ground? (c) At what time t > 0 does the object stop moving? (d) Is the object moving upwards or moving downwards at t = 1? Say why. (e) Find the acceleration function.

Problem 5 2.68 A rigid ball traveling in straight line (the x-axis) hits a solid wall and suddenly rebounds during a brief instant. The vy-t graph shows this Vx (m/s) 30.0 ball's velocity as a function of time. During the first 20.0 s of its motion, find: (a) the total distance the ball moves and (b) its displacement. (c) Sketch a graph of ax-t for this ball's motion. 20.0 (d) Is the graph shown really vertical at 5.0 s? Explain. 10.0 t (s) 5.0 10,0 15.0 20,0 Total distance traveled = 225.0 m a) b) Displacement = -75.0 m %3D -10.0 -20.0

5. A student throws a 0.1 kg ball into the air. (A) Just after the ball leaves their hand, it has a velocity of 5 m/s. (B) At the peak of its motion, it has a velocity of 2 m/s. Assuming no air resistance, to what height dịd the student throw the ball? Also, assume the ball started at h=0 (The zero-reference line is at the starting position of the ball). The energy chart is optional. KE- Vz- Poson A SystemFlow Poston KE- 1.2SJ@ A KE /2..1.2 KE- 0.25 @B Etr E, E Ea Et E, E En Energy Equation KETGPE = KE + GPE 6. A parachutist of mass 50.0 kg jumps out of a stationary balloon at a height of 1,000 meters. The system consists of the parachutist and the Earth, if the parachutist lands with a speed of 5.0 m/s, how much energy was transferred out of the system (so energy transferred to something else)? 7. Suppose the spring below has a spring constant of 50. N/m. The box has a mass of 8.0 kg and rests on a surface of negligible friction. In the diagram above, the spring was compressed 4.0 m.…

Question 3 of 3: Rocky McBlock is a receiver for the Kennesaw Kilowatts in Metro Metric Football League.  In this league all distances on the field are measured in meters, and Rocky always runs straight up and down the field (there is no sideways motion - only motion towards and away from the end zone).  Rocky leaves the line of scrimmage when the ball is snapped and runs forward for 18 meters at a speed of 9 seconds.  He catches the ball and continues to run forward for 16 more meters in 12 seconds, at which point he reaches the end zone. What is his speed before he catches the ball?  What is his speed after he catches the ball?  What is his average speed for the whole play from the time he leaves the line of scrimmage until the time he reaches the end zone?

At a moment when a rocket is 1120 m above the ground, it is traveling straight upward with a speed of 955 m/s. At this instant a small piece detaches from the rocket and begins freefall travel. 1. a) Find the velocity of the piece the instant before it hits the ground. b) Find the time required for it to reach the ground.

You and your friend would like to experimentally determine a value for g, an object's acceleration due to gravity on Earth. Your friend sets a baseball on the edge of a desk, and you crouch down by the floor, waiting for the ball to drop. She pushes the ball off the desk and yells GO! to signal you to press START your phone's stopwatch app. When the ball hits the floor, you press STOP on the app to stop the timer, and see that the time reads t = 0.606 s. Using a tape measure with markings for cm, you measure the top of the desk to be h = 123 cm from the floor.  Part 1) Assuming the ball started with no initial vertical velocity, calculate the value of g in your experiment symbolically. Assume that g is a positive number.  Part 2) Using your previous symbolic answer and the qualities from the experiment, determine a numeric value for g.  Part 3) What is a reasonable quantitative estimate for your uncertainty in stopping the timer, sigma t? What about your error in measuring the height…

M =500kg v16.40 m/s h,-100 m X-110m h. Fk = 250N V-43 m/s The figure depicts the notion of the car from point A to C. If the velocity (Vc)of the car is 16.40 m/s, find the height hc.

The acceleration of a rocket is a = -bV, where V is the speed of exhaust gases coming out of the thruster. What are the SI units of b?