Question

a boy drops a stone from the top of a building 100m high. another boy throws an iron ball, with certain velocity, 2 second later the stone was dropped. calulate the velocity with which iron ball was thrown , so that both the ball and the stone strike the ground at the same time.

Answer 1

Answer:

yes because the stone is dropped there is no force and the iron ball is throwned there is force because the stone take 100s then the iron ball take 50=100 divided 2= 50

Answer 2

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$\huge\bigstar\rm\blue{GIVEN}\bigstar$

For the motion of Stone:-

• $\rm{Initial\:Velocity(u)=0m/s^-1}$

• $\rm{Distance\:travelled(S)=100m}$

• $\rm{Acceleration\:of\:Stone=9.8m/s^{-2}}$.

$\huge\bigstar\rm\blue{Formulae\:Used}\bigstar$

• ${\boxed{\rm{\blue{S=ut+\dfrac{1}{2}g(t)^2}}}}$

Where,

S= Distance

u= Initial Velocity

t =Time

g= Acceleration due to gravity..

Now,

$\implies\rm{S=ut+\dfrac{1}{2}g(t)^2}$

$\implies\rm{100m=0+\dfrac{1}{2}\times{9.8}\times{t}^2}$

$\implies\rm{t^2=\dfrac{200}{9.8}}$

$\implies\rm{t^2=\sqrt{20.4}}$

$\implies\rm{t=4.52s}$

For the motion of iron ball

• $\rm{Initial\:Velocity(u)=0m/s^-1}$

• $\rm{Distance\:travelled(S)=100m}$

• $\rm{Acceleration\:of\:Stone=9.8m/s^{-2}}$.

Time taken by the ball to reach the ground= 4.52-2=2.52s( As it is thrown after 2 second the stone dropped)

• Now, We will find out the Initial Velocity of the iron ball.

$\huge\bigstar\rm\blue{Formulae\:Used}\bigstar$

${\boxed{\rm{\blue{S=ut+\dfrac{1}{2}g(t)^2}}}}$

Where,

S= Distance

u= Initial Velocity

t =Time

g= Acceleration due to gravity..

$\implies\rm\green{S=ut+\dfrac{1}{2}g(t)^2}$

$\implies\rm\green{100=u\times{2.52}+\dfrac{1}{2}\times{9.8}\times{2.52}^2}$

$\implies\rm\green{100=2.52u+4.9\times{6.35}}$

$\implies\rm\green{100=2.52u+31.12}$

$\implies\rm\green{2.52u=100-31.12}$

$\implies\rm\green{u=\dfrac{68.88}{2.52}}$

$\implies\rm\green{u=27.33m/s^{-1}}$

Thus, The iron ball must be thrown with the velocity of 27.33m/s^-1.

MORE TO KNOW:-

• When a Body is dropped freely from a height,it's initial Velocity 'u' is zero.

• When a Body is thrown Vertically Upwards,then at maximum height it Final velocity 'v' is zero.1