Explanation Formula used: 1. Ideal Projectile Motion Equation : “The vector equation of the path for ideal projectile motion is r = ( υ 0 cos α ) t i + ( ( υ 0 sin α ) t − 1 2 g t 2 ) j , where υ 0 is the initial speed and α denotes the angle of elevation. Also the above equation gives the parametric equations x = ( υ 0 cos α ) t and y = ( υ 0 sin α ) t − 1 2 g t 2 , where x is the distance downrange and y is the height of the projectile at time t ≥ 0 .” 2. Height for Ideal Projectile Motion : “The maximum height is given by the equation y max = ( υ 0 sin α ) 2 2 g .” Calculation: It is known that, the time taken by the projectile to attain maximum height is t max = υ 0 sin α g . Compute the three-quarters of maximum height as shown below. y max = ( υ 0 sin α ) 2 2 g 3 4 y max = 3 4 ( υ 0 sin α ) 2 2 g = 3 ( υ 0 sin α ) 2 8 g Now substitute y = ( υ 0 sin α ) t − 1 2 g t 2 in the above equation as follows. ( υ 0 sin α ) t − 1 2 g t 2 = 3 ( υ 0 sin α ) 2 8 g 8 g ( ( υ 0 sin α ) t − 1 2 g t 2 ) = 3 ( υ 0 sin α ) 2 8 g ( υ 0 sin α ) t − 4 g 2 t 2 − 3 υ 0 2 sin 2 α = 0 4 g 2 t 2 − 8 g ( υ 0 sin α ) t + 3 υ 0 2 sin 2 α = 0 By quadratic formula, obtain the value of t as follows

14th Edition

ISBN: 9780135961308

Author: Hass

Publisher: PEARSON CO

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 13.2, Problem 48E

To determine

To show: The time taken by the projectile to attain three-quarters of maximum height is half the time it takes to attain the maximum height.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 47E

Chapter 13.3, Problem 1E

Students have asked these similar questions

EXAMPLE 3 Find S X √√2-2x2 dx. SOLUTION Let u = 2 - 2x². Then du = Χ dx = 2- 2x² = 信 du dx, so x dx = du and u-1/2 du (2√u) + C + C (in terms of x).

Let g(z) = z-i z+i' (a) Evaluate g(i) and g(1). (b) Evaluate the limits lim g(z), and lim g(z). 2-12 (c) Find the image of the real axis under g. (d) Find the image of the upper half plane {z: Iz > 0} under the function g.

k (i) Evaluate k=7 k=0 [Hint: geometric series + De Moivre] (ii) Find an upper bound for the expression 1 +2x+2 where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]

Chapter 13 Solutions

EP THOMAS'CALCULUS,EARLY TRANS.-MYLAB

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

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