Question

at time t=0 s, an object is moving on a horizontal plane with a velocity v0x=1.5 m/s , v0y=3.5 m/s. as the object slides, a constant acceleration acts on it that has the following components: ax=-2.3 m/s^2 and ay=4 m/s^2 . determine the magnitude of the displacement of the object after 2s

Answer 1

Consider the vertical motion,
Initial velocity, voy = 3.5 m/s
Initial acceleration, ay = 4 m/s²
Time taken, t = 2 s

Using the formula, Sy = voy * t + 1/2 * ay * t²,
Substituting values,
Sy = 3.5 * 2 + 0.5 * 4 * 2²
= 15 m
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Consider the horizontal motion,
Initial velocity, vox = 1.5 m/s
Initial acceleration, ax = - 2.3 m/s²
Time taken, t = 2 s

Using the formula, Sx = vox * t + 1/2 * ax * t²,
Substituting values,
Sx = 1.5 * 2 + 0.5 * (- 2.3) * 2²
= - 1.6 m
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Total displacement, S = SQRT[Sx² + Sy²]
= SQRT[15² + (- 1.6)²]
= 15.1 m