Explanation Given information: Orbit radius n R Velocity v 0 Radius of planet R Launch angle θ Final velocity α v 0 Concept used: Following formula will be used. T A + V A = T B + V B Calculation: We know, T A + V A = T B + V B 1 2 m v 2 − g R 2 m R = 1 2 m ( α v 0 ) 2 − g R 2 m n R 1 2 v 2 − g R = 1 2 ( α v 0 ) 2 − g R n Conservation of angular momentum, n R m α v 0 = R m v sin θ v = n α v 0 sin θ So, 1 2 v 2 − g R = 1 2 ( α v 0 ) 2 − g R n 1 2 ( n α v 0 sin θ ) 2 − To determine (b) To prove: the given condition.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 13.2, Problem 13.114P

To determine

(a)

Prove the given condition.

To determine

(b)

To prove: the given condition.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 13.113P

Chapter 13.2, Problem 13.115P

Students have asked these similar questions

Three identical point masses of m = 0.1 (kg) are moving at a constant velocity v=10 (m/s) equidistant from each other on a circular orbit of radius R = 0.4 (m). What is the total angular momentum (kg.m²/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R A m R m A) 0.9 В) 1.2 С) 1.8 D) 3.0 E) 3.6

The two spheres shown collide. the weight of the first sphere (W1) is 40 N while that of the second is (W2) is 30N. assuming that the second sphere's velocity (v2) is 14 m/s and the first sphere's velocity (v1) is 16 m/s along the their respective angles. theta 1(θ1)=30 degrees and theta 2(θ2)=60 degrees. Assume velocities along y will be equal before and after impact. The coefficient of restitution is 0.57. A.) Determine the velocity of the 30N sphere after impact (m/s) B.) Determine the Velocity of the 40N sphere after impact (m/s) C.) Determine the angle of the velocity after impact of the 40N sphere with the horizontal (degrees) D.) Determine the angle of the velocity after impact for the 30N sphere with the vertical (degrees)

2B Show that in a field of attractive forces F(r) a body of mass m can always perform circular motion of radius r0 with constant angular velocity w. Also show that the velocity u of the circular orbit is given by the relation u² == ToF (1) m

Chapter 13 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 1-Ib stone is dropped down the “bottomless pit”...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed the may be...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - A package is projected up a 15° incline at A with...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

(a) Prove the given condition.

Solution Summary: The author explains the formula used to prove the given condition.