Exercises for Question Type 2: Determining with an object given a trajectory passes a specific point - IB | RevisionDojo

IB
Question Type 2: Determining with an object given a trajectory passes a specific point

Question Type 2: Determining with an object given a trajectory passes a specific point Exercises

Question 1

Skill question

Determine whether the trajectory defined by

extbf{r}(t) = (2,3) + tigl(5,-2igr)

passes through the point $(17,-1)$ . If it does, find the corresponding parameter $t$ .

Question 2

Skill question

Does the parameterised curve $extbf{r}(t) = \bigl(\sqrt2\cos t,\ \sqrt2\sin t\bigr)$ pass through $(1,1)$ ? If so, find $t$ in $[0,2\pi)$ .

Question 3

Skill question

Does the circle parameterised by $extbf{r}(t) = igl(3\cos t,\ 3\sin t\bigr)$ pass through $igl(-\tfrac32,\tfrac{3\sqrt3}2\bigr)$ ? Find $t$ .

Question 4

Skill question

A point moves according to

\quad y = 2t + 4, \quad z = 5 - t. $$Does it ever reach $(8, -2, 1)$? If yes, find $t$.

Question 5

Skill question

Does the line

extbf{r}(t) = (1,0,1) + tigl(8,7,2igr)

pass through the point $(17,14,5)$ ? If so, find $t$ .

Question 6

Skill question

A particle moves via

\quad y = 2 - 2t, \quad z = 3 + t. $$Does it ever occupy $(5,-2,5)$? Find $t$ if yes.

Question 7

Skill question

Does the helix

\, \cos t, \, \sin t, \, t) $$pass through $igl( frac12, frac{\sqrt3}{2}, frac\pi3igr)$? Find $t$ if it does.

Question 8

Skill question

Find the parameter $t$ at which the line through $A(1,2,3)$ and $B(4,5,6)$ passes through $C(7,8,9)$ .

Question 9

Skill question

A cycloid is given by

$$Does it pass through $(\pi,2)$? If so, find $t$.

Question 10

Skill question

Determine whether the trajectories

\quad extbf{r}_2(s) = (-1,4,2) + s(3,-1,2)$$ intersect. If so, find $(t,s)$ and the point of intersection.

Question 11

Skill question

A projectile’s position is given by

$$Does it pass through $(10,5,0)$? If yes, find $t$.