Question

A police van moving on a highway with a speed of 30 km h–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h–1. If the muzzle speed of the bullet is 150 m s–1, with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Answer 1

Given,

• $\sf Velocity\:of\:the\:car\:(v_p)=30\:km/h=\dfrac{25}{3}\:m/s$

• $\sf Velocity\:of\:the\:thief\:(v_t)=190\:km/h=\dfrac{160}{3}\:m/s$

• $\sf Velocity\:of\:the\:bullet\:which\:is\:fired\:by\:police\:(v_b)=150\:m/s$

Therefore,

$\sf Final \:velocity\: of \:bullet \:muzzle \:from \:gun = v_b+v_p$

$\implies\sf Final \:velocity\: of \:bullet \:muzzle \:from \:gun = 150+\dfrac{25}{3}$

$\implies \sf Final \:velocity\: of \:bullet \:muzzle \:from \:gun = \dfrac{475}{3}\:m/s$

Let,

• $\sf Velocity\:of\:the\:thief\:(w.r.t.\:thief)=0$

Then,

$\sf Velocity\:of\:the\:bullet\:(w.r.t.\:thief)=v_{b/t}$

$\implies\sf Velocity\:of\:the\:bullet\:(w.r.t.\:thief)=v_b-v_t$

$\implies\sf Velocity\:of\:the\:bullet\:(w.r.t.\:thief)=\dfrac{475}{3}-\dfrac{160}{3}$

$\implies\sf Velocity\:of\:the\:bullet\:(w.r.t.\:thief)=\dfrac{315}{3}$

$\implies\sf Velocity\:of\:the\:bullet\:(w.r.t.\:thief)=105\:m/s$

$\huge\boxed{\bold{\sf Velocity\:of\:the\:bullet=105\:m/s}}$

Additional Information

→ To convert km/h into m/s we have to multiply the given value by  $\bold{\sf \dfrac{5}{18}}$.

→ Speed and velocity are related in much the same way that distance and displacement are related.

→ Speed is a scalar.

→ Velocity is a vector.

→ Both speed and velocity has same unit and dimension.

Answer 2

Answer:

Velocity of police v

p

=30km/h=

3

25

m/s

Velocity of thief v

t

=190km/h=

3

160

m/s

Velocity of bullet which police is fire v

b

=150m/s

final velocity of bullet muzzle from gun =v

b

+v

p

=150+

3

25

=

3

475

m/s

Let velocity of thief is Zero and seen with respect to thief. velocity of bullet w.r.t thief

v

b/t

=v

b

−v

t

=

3

475

−

3

160

=

3

315

=105m/s