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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A hiker inspects a tree frog sitting on a small stick in his hand. Suddenly startled, the hiker drops the slick from rest at a height of 1.85 m above the ground and, at the same instant, the frog leaps vertically upward, pushing the stick down so that it hits the ground 0.450 s later. Find the height of the frog at the instant the stick hits the ground if the frog and the stick have masses of 7.25 g and 4.50 g, respectively. (Hint: Find the center-of-mass height at t = 0.450 s for the frog-stick system and then use) the definition of center of mass to solve for the frog’s height.)

To determine
The height of the frog at the instant the stick hits the ground.

Explanation
Consider the positive y axis starts from the ground and the center of mass of the frog-stick system as particle in free fall dropped from the height of 1.85m zero initial speed. At the time 0.450s the stick hits the ground, the center of mass of the system is to be calculated. From this information, the height of the frog has to be calculated at instant the stick hits the ground.

Given info: The mass of the frog is 7.25g , the mass of the stick is 4.50g , the initial height of frog-stick system is 1.85m , the instant at which the stick hits the ground is 0.450s .

The formula for the height of the center of mass of the frog-stick system is,

ycm=y0+v0t12gt2

  • y0 is initial height of the frog-stick system
  • v0 is initial speed of the frog-stick system
  • t is the time at which the stick that hits the ground
  • g is acceleration due to gravity

Substitute 1.85m for y0 , 0m/s for v0 , 0.450s for t , and 9.80m/s2 for g to find ycm .

ycm=1.85m+(0m/s)(0.450s)12(9.80m/s2)(0.450s)2=0.858m

Thus, the height of the frog-stick system is 0.858m .

Section2:

To determine: The height of the frog at the instant the stick hits the ground.

Answer: The height of the frog at the instant the stick hits the ground is 1

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