The figure above shows two objects, P and Q moving with velocities 30 m s

^{-1}and 20 m s

^{-1}respectively towards each other on a straight line.

How long, after that instant, will P and Q meet?

A. 100.0 s

B. 83.3 s

C. 20.0 s

D. 13.3 s

__Solution__Show solution >>

The answer is C.

Let the distance travelled by P and Q before they meet each other be

Since we know the speeds of P and Q, their distance travelled is the product of their speed and time taken,

Substituting in equation (1),

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Let the distance travelled by P and Q before they meet each other be

*d*_{1 }and*d*_{2 }respectively. Here, we can form an equation:d_{1 }+ d_{2} | _{}= 1000 m | |

d_{1} | = 1000 m - d_{2 } | - (1) |

Since we know the speeds of P and Q, their distance travelled is the product of their speed and time taken,

*t*.*t*is also the time when P and Q meet.*d*_{1 }= (30 m s^{-1})*t**d*_{2 }*=*(20 m s^{-1})*t*Substituting in equation (1),

d_{1} | = 1000 m - d_{2} |

(30 m s^{-1})t 50 t m s^{-1}∴ t | = 1000 m - (20 m s^{-1})t= 1000 m = 20 s |

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**Question source:**Malaysia National Physics Competition Panel

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