Motion in a Plane - Result Question 28

31. A bullet is fired from a gun with a speed of 1000 $m / s$ in order to hit a target $100 m$ away. At what height above the target should the gun be aimed? (The resistance of air is negligible and $.g=10 m / s^{2})$

[1995]

(a) $5 cm$

(b) $10 cm$

(c) $15 cm$

(d) $20 cm$

Topic 3: Projectile Motion

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Answer:

Correct Answer: 31. (a)

Solution:

  1. (a) Speed of the bullet (v) $=1000 m / s$ and horizontal distance of the target $(s)=100 m$. Time taken to cover the horizontal distance $(t)$ $=\frac{100}{1000}=0.1 sec$.

During this time, the bullet will fall down vertically due to gravitational acceleration.

$\therefore$ height $(h)=u t+\frac{1}{2} g t^{2}$

$ \begin{aligned} & =(0 \times 0.1)+\frac{1}{2} \times 10(0.1)^{2} \\ & =0.05 m=5 cm \end{aligned} $