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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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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GOAL Solve a problem involving a powered ascent Maximum followed by free-fall motion. height Jmax v= 0 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 y = 0 Launch and has an acceleration of -9.80 m/s², with initial Two 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.
Transcribed Image Text:GOAL Solve a problem involving a powered ascent Maximum followed by free-fall motion. height Jmax v= 0 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 y = 0 Launch and has an acceleration of -9.80 m/s², with initial Two 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 the second phase ending at the maximum height and the third phase a free fall from maximum height to the ground. Although this approach gives the correct answer, it's an unnecessary complication. Two phases are sufficient, one for each different acceleration. QUESTION If, instead, some fuel remains, at what height should the engines be fired again to brake the rocket's fall and allow a perfectly soft landing? (Assume the same acceleration as in the initial descent.) PRACTICE IT Use the worked example above to help you solve this problem. A rocket moves straight upward, starting from rest with an acceleration of +25.9 m/s?. It runs out of fuel at the end of 5.22 s and continues to coast 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/s m (b) Find the maximum height the rocket reaches. (c) Find the velocity the instant before the rocket crashes on the ground. m/s EXERCISE HINTS: 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 at rest. At a height of 86.2 m, the rocket's engines start and provide constant upward acceleration until the rocket lands. What acceleration is required if the speed on touchdown is to be zero? (Neglect air resistance.) |m/s2
Transcribed Image Text:REMARKS You may think that it is more natural to break this problem into three phases, with the second phase ending at the maximum height and the third phase a free fall from maximum height to the ground. Although this approach gives the correct answer, it's an unnecessary complication. Two phases are sufficient, one for each different acceleration. QUESTION If, instead, some fuel remains, at what height should the engines be fired again to brake the rocket's fall and allow a perfectly soft landing? (Assume the same acceleration as in the initial descent.) PRACTICE IT Use the worked example above to help you solve this problem. A rocket moves straight upward, starting from rest with an acceleration of +25.9 m/s?. It runs out of fuel at the end of 5.22 s and continues to coast 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/s m (b) Find the maximum height the rocket reaches. (c) Find the velocity the instant before the rocket crashes on the ground. m/s EXERCISE HINTS: 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 at rest. At a height of 86.2 m, the rocket's engines start and provide constant upward acceleration until the rocket lands. What acceleration is required if the speed on touchdown is to be zero? (Neglect air resistance.) |m/s2
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