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
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The answer is C.
Let the distance travelled by P and Q before they meet each other be d1 and d2 respectively. Here, we can form an equation:
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.
d1 = (30 m s-1)t
d2 = (20 m s-1)t
Substituting in equation (1),
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Let the distance travelled by P and Q before they meet each other be d1 and d2 respectively. Here, we can form an equation:
| d1 + d2 | = 1000 m | |
| d1 | = 1000 m - d2 | - (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.
d1 = (30 m s-1)t
d2 = (20 m s-1)t
Substituting in equation (1),
| d1 | = 1000 m - d2 |
| (30 m s-1)t 50t 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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