Question 216: Laws of Motion

Question

A bullet from a gun is fired on a rectangular wooden block with velocity $$u$$. When bullet travels $$24 \mathrm{~cm}$$ through the block along its length horizontally, velocity of bullet becomes $$\frac{u}{3}$$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

Accepted Answer

$$B y v^{2}=u^{2}+2 a s$$
$$\left(\frac{u}{3}\right)^{2}=u^{2}-2 a x$$
$$2 a x=u^{2}-\frac{u^{2}}{9}$$
$$2 \mathrm{ax}=\frac{8 \mathrm{u}^{2}}{9}$$ ..... (1)
Similarly from starting
$$v^{2}=u^{2}+2 a x$$
$$0=u^{2}-2 a x_{2}$$
$$2 \mathrm{ax}_{2}=\mathrm{u}^{2}$$ ..... (2)
$$\mathrm{By}~(1) /(2)$$
$$\frac{x}{x_{2}}=\frac{8}{9}$$
$$\frac{24}{x_{2}}=\frac{8}{9}$$
$$\mathrm{x}_{2}=27 \mathrm{~cm}$$

Answer

$$24 \mathrm{~cm}$$

Answer

$$28 \mathrm{~cm}$$

Answer

$$30 \mathrm{~cm}$$

Answer

$$27 \mathrm{~cm}$$

Laws of Motion

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