Question

At 6 safter 3:00, a butterfly is observed leaving a flower whose location is$<6,-3,10>\mathbf{m}$relative to an origin on top of a nearby tree. The butterfly flies until 10 safter 3:00, when it alights on a different flower whose location is$<6.8,-4.2,11.2>\mathbf{m}$ relative to the same origin. What was the location of the butterfly at a time 8.5 safter 3:00? What assumption did you have to make in calculating this location?

Short answer

The location of the butterfly at a time 8.5s is .

The assumption made in this question is that the average velocity is constant.

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The initial location of butterfly is, .
• Time at which the butterfly was at initial location is, 6 s.
• The final location of the butterfly is, .
• Time by which the butterfly reached to the final location is, 10 s.

 Step 2: Significance of Newton’s first law in calculating the distances

This law states that a body will continue to proceed at a uniform velocity if no external force acts on that body.

The equation of the average velocity and the displacement gives the location of the butterfly.

Determination of the average velocity of the butterfly

The equation of the average velocity of the butterfly can be expressed as follows,

${\mathrm{v}}_{\mathrm{avg}}=\frac{{\mathrm{r}}_2-{\mathrm{r}}_1}{{\mathrm{t}}_2-{\mathrm{t}}_1}$

Here, v_avg is the average velocity, r₁ is the initial location of butterfly, r₂ is the final location of the butterfly, t₁ is the time taken by the butterfly to reach to the initial location and t₂ is the time taken by butterfly to reach at the final location.

For data-custom-editor="chemistry" , data-custom-editor="chemistry" , data-custom-editor="chemistry" ${\mathrm{t}}_1=6\mathrm{s}$and data-custom-editor="chemistry" ${\mathrm{t}}_2=10\mathrm{s}$.

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Determination of the location of the butterfly

The equation of displacement of the butterfly is expressed as follows,

$\mathrm{s}={\mathrm{s}}_0+{\mathrm{v}}_{\mathrm{avg}}\mathrm{t}$

Here, s is the displacement of the butterfly, s₀ is the initial displacement of the butterfly, v_avg is the average velocity of the butterfly, and t is the time taken by the butterfly to reach the final location.

For , and $\mathrm{t}=10\mathrm{s}-8.5\mathrm{s}=1.5\mathrm{s}$.

Thus, the location of the butterfly at a time 8.5 s is .

The assumption made in this question is that the average velocity is constant as the velocity may have changed with time. But here it is taken as constant.

Thus, the assumption made in this question is that the average velocity is constant.