Question

At a point on the ground a man throws a ball horizontally with an inclination 60 degree to the horizontal. At the same instant a boy starts running with the half the speed of the ball to catch it. Will the boy catch the ball?

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Secondary School Physics 13 points

A boy throws a ball with a velocity vo at an angle alpha to the horizontal .at the same instant he starts running with uniform velocity to catch the ball before it hits the ground .to achieve this,he should run with a velocity of-

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NavaN11

NavaN11 Virtuoso

So, this is a very interesting question from the projectile motion

Now,

Let us start from the basics,

Considering the boy was at rest while throwing the ball(not running or anything)

So, as the ball is thrown at an at an angle α the horizontal component of velocity will be vcosα and the vertical component will be vsinα

(I am assuming Vo as asked in your question as v)

Let Vx= vcosα

then,

Vy=vsinα

Now, the range of projectile will be ( 2 × Vx × Vy )/g

which will be equal to,

R=( v² × sin2α )/g............... 1

And the time taken will be,

T=(2 × Vx)/g.................2

which will be equal to,

T=( 2× v sinα )/g

So, if he wants to catch the ball then the velocity with which he should run is..

=(Displacement)/(Time)

=Equation 1 divided by equation 2

=(sin2α)/(2sinα)

=(2 ×v× sinα ×cosα )/(2 sinα )

=v cosα

(This line after derivation in short means that horizontal component of the velocity should be the same)

(Since boy was running in horizontally only...so his velocity should be equal to horizontal component of the ball)