Question

155. A particle is projected vertically upwards and it
attains maximum height H. If the ratio of times to
attain height h (< H) is 1/3; then h equals
(a) (2/3) H
(b) (3/4) H
(©) (4/3) H
(d) (3/2) H​

Answer 1

Answer:

Total time taken to reach height H=t=

g

2H

​

​

Initial velocity=u=

2gH

​

Time to reach height h=t

1

​

=t/3=

3

1

​

 

g

2H

​

​

Now by second equation of motion

⇒h=ut

1

​

+0.5×(−g)(t

1

2

​

)

⇒h=

2gH

​

×$$\dfrac{1}{3}\times  \sqrt{\dfrac{2H}{g}}$$−0.5×g×(

3

1

​

 

g

2H

​

​

)

2

⇒h=

3

2H

​

−

9

H

​

=

9

5H

​

⇒

H

h

​

=

9

5

​