Question

An aeroplane is flying vertically upwards with a uniform speed of $500m/s$ When it is at a height of $1000m$ above the ground a shot is fired at it with the speed of $700m/s$ from a point directly below it.The minimum uniform acceleration of the aeroplane now so that it may escape from being hit?[$g=10m/s^2$]

• A. $10m/s^2$
• B. $8m/s^2$
• C. $12m/s^2$
• D. $Noneofthese$

Answer 1

The correct option is A $10m/s^2$

$x\ge y$ ( to avoid hit)

$1000+500t+\frac{1}{2}a{t}^2\ge 700t-\frac{1}{2}g{t}^2$

$2000+1000t+a{t}^2\ge 1400t-10t^2$

$(10+a)t^2-400t+2000\ge 0$

For a quadratic equation to have no real solution $D<0$

$(400{)}^2-4.(10+a).2000<0$

$400\times 400<4(10+a)2000$

$10+a>20$

$a>10m/s^2$