To determine The launch angle that results in the maximum range up the incline of angle. The launch angles at incline of angles of 0 ° , 30 ° and 45 ° . Explanation Write the horizontal component of initial velocity of the projectile. v x 0 = v 0 cos θ Here, horizontal component of initial velocity of the projectile is v x 0 , initial velocity of the projectile is v 0 and angle at which the projectile is launched is θ . Write the vertical component of initial velocity of the projectile. v y 0 = v 0 cos θ Here, vertical component of initial velocity of the projectile is v y 0 . Write the equation for horizontal distance travelled by the projectile. x = x 0 + v x 0 t (I) Here, horizontal distance travelled by the projectile is x , initial horizontal distance travelled by the projectile is x 0 and time taken to reach the required location is t . Write the equation for vertical distance travelled by the projectile. y = y 0 + v y 0 t − 1 2 g t 2 (II) Here, vertical distance travelled by the projectile is y , initial vertical distance travelled by the projectile is y 0 and acceleration due to gravity is g . Conclusion: Substitute R cos α for x , 0 for x 0 and v 0 cos θ for v x 0 in Equation (I). R cos α = 0 + ( v 0 cos θ ) t R cos α = v 0 cos θ t t = R cos α v 0 cos θ Substitute R sin α for y , 0 for y 0 , R cos α v 0 cos θ for t and v 0 sin θ for v y 0 in Equation (II). R sin α = 0 + ( v 0 sin θ ) ( R cos α v 0 cos θ ) − 1 2 g ( R cos α v 0 cos θ ) 2 R sin α = sin θ ( R cos α cos θ ) − 1 2 g ( R 2 ( cos α ) 2 v 0 2 ( cos θ ) 2 ) 1 = tan θ tan α − 1 2 g sin α ( R ( cos α ) 2 v 0 2 ( cos θ ) 2 ) 1 − tan θ tan α = − 1 2 g sin α ( R ( cos α ) 2 v 0 2 ( cos θ ) 2 ) − 2 v 0 2 g ( 1 − tan θ tan α ) = ( R ( cos α ) 2 sin α ( cos θ ) 2 ) R = − 2 v 0 2 g ( sin α ( cos θ ) 2 ( cos α ) 2 ) ( 1 − tan θ tan α ) = 2 v 0 2 g ( − sin α ( cos θ ) 2 ( cos α ) 2 + ( tan θ tan α ) sin α ( cos θ ) 2 ( cos α ) 2 ) = 2 v 0 2 g ( ( tan θ

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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 2.4, Problem 95P

To determine

The launch angle that results in the maximum range up the incline of angle.

The launch angles at incline of angles of 0°, 30° and 45°.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.4, Problem 94P

Chapter 2.4, Problem 96P

Students have asked these similar questions

36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

Can you solve this for me?

5670 mm The apartment in the ground floor of three floors building in Fig. in Baghdad city. The details of walls, roof, windows and door are shown. The window is a double glazing and air space thickness is 1.3cm Poorly Fitted-with Storm Sash with wood strip and storm window of 0.6 cm glass thickness. The thickness of door is 2.5 cm. The door is Poor Installation. There are two peoples in each room. The height of room is 280 cm. assume the indoor design conditions are 25°C DBT and 50 RH, and moisture content of 8 gw/kga. The moisture content of outdoor is 10.5 gw/kga. Calculate heat gain for living room : الشقة في الطابق الأرضي من مبنى ثلاثة طوابق في مدينة بغداد يظهر في مخطط الشقة تفاصيل الجدران والسقف والنوافذ والباب. النافذة عبارة عن زجاج مزدوج وسمك الفراغ الهوائي 1.3 سم ضعيف الاحكام مع ساتر حماية مع إطار خشبي والنافذة بسماكة زجاج 0.6 سم سماكة الباب 2.5 سم. الباب هو تركيب ضعيف هناك شخصان في كل غرفة. ارتفاع الغرفة 280 سم. افترض أن ظروف التصميم الداخلي هي DBT25 و R50 ، ومحتوى الرطوبة 8…

Chapter 2 Solutions

Engineering Mechanics: Dynamics

Ch. 2.2 - Prob. 1P Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Prob. 9P Ch. 2.2 - A particle in an experimental apparatus has a...

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.

The launch angle that results in the maximum range up the incline of angle. The launch angles at incline of angles of 0 ° , 30 ° and 45 ° .

Concept explainers

Videos

The launch angle that results in the maximum range up the incline of angle. The launch angles at incline of angles of 0°, 30° and 45°.

Want to see the full answer?

Chapter 2 Solutions

The launch angle that results in the maximum range up the incline of angle.

The launch angles at incline of angles of 0°, 30° and 45°.