Question

Example IO The maximum height attained by a projectile is increased by 10% by increasing
its speed of projection, without changing the angle of projection. What will the percentage inerease in
the horizontal range.​

Answer 1

Answer:

Let the initial velocity of projection be ‘u’, the initial angle of projection ‘θ’ and time of flight be ‘t’.

Initial max. height is, h=

2g

(u

2

sin

2

θ)

Time of flight,t=

g

2usinθ

⇒t

2

=

g

2

4u

2

sin

2

θ

⇒t

2

=(

g

8

)[

2g

(u

2

sin

2

θ)

]=(

g

8

)h

Therefore,

t

2

T

2

=

h

H

Now, new height, H=h+(

100

10

)h=(

10

11

)h

⇒

h

H

=

10

11

And,

t

2

T

2

=

10

11

⇒

t

T

=1.05

⇒

t

T

–1=0.05

⇒(T−t)t=0.05

⇒(T−t)t×100=5%

Thus, the % increase in time of flight is 5%.