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# Answer to Question #103948 in Mechanics | Relativity for havefun7741

Question #103948
A car of negligible size is travelling from A to B with 5 s, from B to C with 4 s, from C to D with 3 s, then the car rolls off at D in projectile motion to cross the pit EF. The angles of AB and CD with horizontal are given as 30° and 50° respectively.(a) (i) Find the average speed from A to D.(ii) Find the displacement from A to D in unit vector form.(iii) Find the average velocity from A to D in unit vector form.(iv) Find the magnitude and angle (with horizontal) of the average velocity from A to D.
1
2020-02-28T10:15:05-0500

Draw the trajectory (as if we are in a helicopter or satellite):

i. If the car moves at a constant speed, the average speed is the total distance over total time: the distance is

"v(5+4+3)=12v,"

the time is

"t=12 \\text{ s}."

"v_{av}=\\frac{12v}{12}=v."

ii. Find the magnitudes:

Therefore:

"\\vec{r}=\\vec{r}_{AB}+\\vec{r}_{BC}+\\vec{r}_{CD}=10.3v\\textbf{i}+4.8v\\textbf{j}."

iii, iv. Calculate the angle:

The magnitude is v. Therefore:

"\\vec{v}=v(\\text{sin}\\alpha\\textbf{i}+\\text{ cos}\\alpha\\textbf{j})=0.3v\\textbf{i}+0.95v\\textbf{j}."

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