GOAL Solve a problem involving a powered ascentMaximumfollowed by free-fall motion.height Jmaxv= 0PROBLEM A rocket moves straight upward, startingfrom rest with an acceleration of +29.4 m/s?. It runsout of fuel at the end of 4.00 s and continues to coastupward, reaching a maximum height before falling backPhase 2a= -9.80 m/s2to Earth. (a) Find the rocket's velocity and positionat the end of 4.00 s. (b) Find the maximum heightthe rocket reaches. (c) Find the velocity the instantbefore the rocket crashes on the ground.Rocket+yfuelSTRATEGY Take y = 0 at the launch point and yburnspositive upward, as in the figure. The problem consistsoutPhase 1a = 29.4 m/s2"of two phases. In phase 1 the rocket has a net upwardacceleration of 29.4 m/s?, and we can use the kinematicequations with constant acceleration a to find the heightRocket crashesafter fallingfrom Jmaxand velocity of the rocket at the end of phase 1, whenthe fuel is burned up. In phase 2 the rocket is in free fally = 0Launchand has an acceleration of -9.80 m/s², with initialTwo linked phases of motion for a rocket that is launched,uses up its fuel, and crashes.velocity and position given by the results of phase 1.Apply the kinematic equations for free fall. REMARKS You may think that it is more natural to break this problem into three phases, with thesecond phase ending at the maximum height and the third phase a free fall from maximum height to theground. Although this approach gives the correct answer, it's an unnecessary complication. Two phases aresufficient, one for each different acceleration.QUESTION If, instead, some fuel remains, at what height should the engines be fired again to brakethe rocket's fall and allow a perfectly soft landing? (Assume the same acceleration as in the initialdescent.)PRACTICE ITUse the worked example above to help you solve this problem. A rocket moves straight upward, startingfrom rest with an acceleration of +25.9 m/s?. It runs out of fuel at the end of 5.22 s and continues tocoast upward, reaching a maximum height before falling back to Earth.(a) Find the rocket's velocity and position at the end of 5.22 s.V, =m/sm(b) Find the maximum height the rocket reaches.(c) Find the velocity the instant before the rocket crashes on the ground.m/sEXERCISEHINTS: GETTING STARTED I I'M STUCK!An experimental rocket designed to land upright falls freely from a height of 2.71 x 102 m, starting atrest. At a height of 86.2 m, the rocket's engines start and provide constant upward acceleration until therocket lands. What acceleration is required if the speed on touchdown is to be zero? (Neglect airresistance.)|m/s2

A rocket ,starting from rest, accelerates upwards with an acceleration of 29.4 m/s2 , by burning its…

GOAL Solve a problem involving a powered ascent Maximum height Jmax v= 0 followed by free-fall motion. PROBLEM A rocket moves straight upward, starting from rest with an acceleration of +29.4 m/s?. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back Phase 2 a=-9.80 m/s2 to Earth. (a) Find the rocket's velocity and position at the end of 4.00 s. (b) Find the maximum height the rocket reaches. (c) Find the velocity the instant before the rocket crashes on the ground. Rocket +y fuel STRATEGY Take y = 0 at the launch point and y burns positive upward, as in the figure. The problem consists out Phase 1 a = 29.4 m/s2 of two phases. In phase 1 the rocket has a net upward acceleration of 29.4 m/s?, and we can use the kinematic equations with constant acceleration a to find the height Rocket crashes after falling from Jmax and velocity of the rocket at the end of phase 1, when the fuel is burned up. In phase 2 the rocket is in free fall Launch

GOAL Solve a problem involving a powered ascent Maximum height Jmax v= 0 followed by free-fall motion. PROBLEM A rocket moves straight upward, starting from rest with an acceleration of +29.4 m/s?. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back Phase 2 a=-9.80 m/s2 to Earth. (a) Find the rocket's velocity and position at the end of 4.00 s. (b) Find the maximum height the rocket reaches. (c) Find the velocity the instant before the rocket crashes on the ground. Rocket +y fuel STRATEGY Take y = 0 at the launch point and y burns positive upward, as in the figure. The problem consists out Phase 1 a = 29.4 m/s2 of two phases. In phase 1 the rocket has a net upward acceleration of 29.4 m/s?, and we can use the kinematic equations with constant acceleration a to find the height Rocket crashes after falling from Jmax and velocity of the rocket at the end of phase 1, when the fuel is burned up. In phase 2 the rocket is in free fall Launch

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter3: Motion Along A Straight Line

Section: Chapter Questions

Problem 70P: Unreasonable results A dolphin in an aquatic show jumps straight up out of the water at a velocity...

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