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An aeroplane flying vertically upwards with a uniform speed of 500m/s. when it is at height of 1000m above ground a shot is fired at it with a speed of 700m/s from a point directly below it.The minimum uniform acceleration of aeroplane now so that it may escape from being hit? An aeroplane flying vertically upwards with a uniform speed of 500m/s. when it is at height of 1000m above ground a shot is fired at it with a speed of 700m/s from a point directly below it.The minimum uniform acceleration of aeroplane now so that it may escape from being hit?
For aeroplane,from first eqn.v = u – gt500 = 700 – gtt = 20 s.and in this time, h = 700*20 – 0.5g*400 = 12000mtotal distamce = 12000 – 1000 = 11000 meter.apply s = ut + 0.5at^2for s= 11k meter and at t= 20 s and u = 500 m/s.find a.
Velocity of bullet wrt plane = 700 -500 = 200m/sLet the acceleration of plane be a.As the bullet is going upward so acceleration of bullet is g downwardsSo acceleration of bullet wrt plane = -g-a = -10-aThe bullet will not hit the when its vel is min i.e v=0So from v2 =u2+2as0=200 2 +2(-10-a) 10000=40000+2000(-10-a)a= 10m/s2
Velocity of bullet with respect to the plane = 700 -500 = 200m/sLet the acceleration of plane be a.As the bullet is going upward so acceleration of bullet is g downwardsSo acceleration of bullet with respect to the plane = -g-a = -10-aThe bullet will not hit the when its velocity is minimum that is v=0So from v2 =u2+2as0=200 2 +2(-10-a) 10000=40000+2000(-10-a)a= 10m/s2
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