Question

The graph between maximum height attained and the time of flight of a particle thrown vertically upward with a variable speed will be
a. straight line
b. parabola
c. ellipse
d. hyperbola​

Answer 1

Given : The graph between maximum height attained and the time of flight of a particle thrown vertically upward with a variable speed  

To Find : Shape of Graph

a. straight line

b. parabola

c. ellipse

d. hyperbola​

Solution

Let say speed = U

Time to reach maximum height =  t

using V = U + at

=> 0 = U  - gt

=> t = U/g

Time of flight = 2t

= 2U/g

S = ut  + (1/2)at²

H = U(U/g)  + (1/2)(-g)(U/g)²

=> H = U²/g  -  U²/2g

=> H = U²/2g

=> H = U  . U/2g

=> H =  UT/4

=> H = (U/4) T

   

T = 2U/g

H = U²/2g

H ∝ T²

Hence Parabola

graph between maximum height attained and the time of flight of a particle thrown vertically upward with a variable speed will be  

parabola

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The graph between maximum height attained

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