5. Consider projectile motion with air resistance taken into account. If the resistance is proportional to thevelocity, the initial velocity has vertical and horizontal components Voy and Vox, respectively, and the motionstarts at the origin, show that the trajectory is given byy[x]gx- V² In (1 - 0x) + (Poy - V) x.gVox

Projectile motion with air resistance is a classical mechanics problem that involves studying the…

Answered: 5. Consider projectile motion with air…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter5: Displacement And Force In Two Dimensions

Section: Chapter Questions

Problem 75A

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Similar questions

Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?
Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?
What do vectors and scalars have in common? How do they differ?
In a later chapter, you will find that the weight of a particle varies with altitude such that w=mgr02r2where r0is the radius of Earth and ris the distance from Earth’s center. If the particle is fired vertically with velocity v0from Earth’s surface, determine its velocity as a function of position r. (Hint: use adr=vdv, the rearrangement mentioned in the text.)
A ball is thrown at an initial height of 50 feet at an initial velocity of 65 feet/second at an angle of 75 degrees. Given the parametric equations y - 16t2 + Vo Sin(0)t + ho and x = Vo. Cos(0)t. When doing calculations, carry 5 digits of accuracy, so your round off does not build up. a. What is the ball's height in 2 seconds? 111.57035 v o feet. b. When will the object hit the ground? 4.60298 v o seconds. c. How far horizontally will the ball be when it hits the ground? 77.43702 v o feet. d. When will the ball be at its maximum height? 1.96204 o seconds. e. What is the ball's maximum height? 4.61479 x feet. feet f. How far horizontally will the ball be when it reaches its maximum height? 77.63571 ×
1110. In Fig. P-1109, a ball thrown down the incline strikes it at a distance s 254.5 It. If the ball rises to a maximum height h 64.4 ft above the point of release, compute its initial velocity vo and inclination 6. Ans. v. = 80.5 ft per see; 0= 53.1° FIG. P-1109 and P-1110.
b. Prove that, the range, R the time of flight, T and the Maximum height, H by a projectile are respectively given by; vỷ sin² e R = (5/g) sin20 , T = (2v,sin®), and H = 2g
Question 4: A particle is thrown into air with initial speed vo making angle 0 with the horizontal as shown in Figure 1. The gravitational acceleration g and a constant acceleration a, due to a wind act on the particle. Find the range of the motion. aw Figure 1 Select one: vž sin 0 cos 0 2a,,v3 sin? 0 g? vở sin(20) 2a,vž sin? 0 -2v sin 0 cos 0 awv sin(20) 2g2 2v3 sin 0 cos e auvổ sin(20)
H.W: A ball is thrown with an initial speed voat an angle 0 below the horizontal from rooftop 44m above the ground. It lands 2sec later at a point Vor 32m from the base of the building. Find v, and 0 Ans. 0 = -37.32v, = 20. 1m/s %3D 44y
Question 4: A particle is thrown into air with initial speed vo making angle 0 with the horizontal as shown in Figure 1. The gravitational acceleration g and a constant acceleration a, due to a wind act on the particle. Find the range of the motion. a, 'w Figure 1 100
Let W = (x²y, y³z, xyz). Determine V.Ŵ.
H.W: A ball is thrown with an initial speed vat an angle e below the horizontal from rooftop 44m above the ground. It lands 2sec later at a point 32m from the hase of the building. Find v, and e Ans. 8 = -37.32v, = 20. 1m/s

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