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Scrat
16 days ago
12

two kittens are on opposite sides of a field, 250 m apart. kitten the runs at a constant speed of 25 m/s due east on a collision

course with kitten b, which is traveling west at 12 m/s. how much time elapses before the two kittens collide?

Physics
1 answer:
ValentinkaMS [1.1K]16 days ago
3 0

Set the initial location of kitten A on the left side of the field (designated as point A) at the origin, running east which is the positive direction. Kitten B starts at position {x_B}_0=250\,\mathrm m, while kitten A’s beginning spot is {x_A}_0=0\,\mathrm m.

Kitten A moves with a velocity of v_A=25\,\dfrac{\mathrm m}{\mathrm s}, and kitten B with v_B=-12\,\dfrac{\mathrm m}{\mathrm s}. Their positions over time are described by

x_A=\left(25\,\dfrac{\mathrm m}{\mathrm s}\right)t

x_B=250\,\mathrm m+\left(-12\,\dfrac{\mathrm m}{\mathrm s}\right)t

The collision occurs when the positions are the same, i.e. when x_A=x_B. Solving this gives

\left(25\,\dfrac{\mathrm m}{\mathrm s}\right)t=250\,\mathrm m+\left(-12\,\dfrac{\mathrm m}{\mathrm s}\right)t

\implies\left(37\,\dfrac{\mathrm m}{\mathrm s}\right)t=250\,\mathrm m

\implies t=\dfrac{250\,\mathrm m}{37\,\frac{\mathrm m}{\mathrm s}}=6.76\,\mathrm s

Which results in approximately 6.8 seconds, considering significant figures.

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