Two bodies move according to the laws x1 = 3t + 0.5t ^ 2 and x2 = 12-6t. Determine the time and place of the meeting
September 24, 2021 | education
| x1 (t) = 3 * t + 0.5 * t ^ 2.
x2 (t) = 12 – 6 * t.
xbс -?
tbс -?
The bodies will meet at that moment in time when they have the same coordinates: x1 (t) = x2 (t).
3 * tbc + 0.5 * tbc ^ 2 = 12 – 6 * tbc.
0.5 * tbc ^ 2 + 9 * tbc – 12 = 0 – quadratic equation.
tbс ^ 2 + 18 * tbс – 24 = 0.
Let’s find the discriminant: D = 182 – 4 * (- 24) = 420.
tвс1,2 = (-18 ± √420) / 2.
tвс1 = 1.25 s, tвс ^ 2 = – 18 s – the root does not make sense.
hvs = 3 * 1.25 + 0.5 * (1.25) ^ 2 = 4.5 m.
xvs = 12 – 6 * 1.25 = 4.5 m.
Answer: the bodies will meet through tvs = 1.25 s, hvs = 4.5 m.
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