IIT JEE , AIEEE Forum - Physics , Mechanics

surya_kant_2005

An aeroplane is flying vertically upwards with a uniform speed of 500 m/s. When it is at a height of 1000 m above the ground a shot is fired at it with a speed of 700 m/s from a point directly below it. What should be the minimum acceleration of the aeroplane so that it may escape from being hit ?

vineet

Hey surya u gave dat aeroplane is movin with constant speed & again askin to find acceleration of aeroplane ???

surya_kant_2005

Vineet,

I think that u got b dum to think like that. I am not asking about its acceleration. I am asking the minimum accelation required to escape the bullet.

One more thing I like ur signature- "THINK DIFFERENT......THINK APPLE". But I think u should eat apple rather than only thinking abut it.

Sorry Buddy but I hate stupid answers.

Bye

KAB

Let the bullet meet the plane after the plane travelled a distance x with acceleration a in time t.

For plane:

x=500t+(at²)/2

For bullet:

1000+x=700t-5t² (g=10m/s²)

So 1000+500t+(at²)/2=700t-5t² ..........(1)

Now differentiate (1) wrt t and put da/dt=0 for acceleration to be minimum.

You will get t=200/(10+a).

Substitute for t in (1) and solve.

You will get a=10m/s²

This is the minimum acceleration of the plane to just escape from the bullet.

gupta

HI KAB (608)
YOU said sbstitute the value of t in 1but you didnot gave the value of t ?????

t should be equal to 70 sec (taking g =10 for bullet to stop)

for this value of t required ace comes to be negative?????????

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