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Answer: A grasshopper leaps into the air from the edge of

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors:  Hugh D. Young; Roger A. Freedman; A. Lewis Ford ISBN: 9780321696861 89

Solution for problem 63P Chapter 3

Sears and Zemansky's University Physics with Modern Physics | 13th Edition

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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors:  Hugh D. Young; Roger A. Freedman; A. Lewis Ford

Sears and Zemansky's University Physics with Modern Physics | 13th Edition

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Problem 63P

A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.57. Find (a) the initial speed of the grasshopper and (b) the height of the cliff.

Step-by-Step Solution:

Solution 63P

Step 1 of 5:

(a) the initial speed of the grasshopper

Let us consider vertical component of velocity,

                                        

where,as it reaches max height, its final velocity will be zero,

Initial velocity =v sin 50,

distance s=  6.74 cm = 0.0674 m

Acceleration , a=g=

Substituting given data in above equation,

                                

                                

v = 1.5 m/s

Therefore, the initial velocity of the grasshopper is  1.5 m/s.

Step 2 of 5:

(b) the height of the cliff.

Using fundamental relation of speed,

For horizontal component,

Time of flight,                                        t=

Substituting distance(horizontal)= 1.06 m and speed(horizontal component), v= v cos 50

                                                t=

Using v = 1.5 m/s

t=

t = 1.099 s

Step 3 of 5:

Time taken to reach maximum height(vertical component),         

Using v = 1.5 m/s

0.1175 s

Step 4 of 5

Chapter 3, Problem 63P is Solved
Step 5 of 5

Textbook: Sears and Zemansky's University Physics with Modern Physics
Edition: 13
Author: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
ISBN: 9780321696861

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