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

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

Question 1

A particle's position at time t is given by the parametric equations x = 1 + 4 t, y = 2 - 2 t, z = 3 + t Determine whether there is a value of t for which the particle occupies the point (5, - 2, 5) .

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Question 2

A point moves according to the parametric equations x = 3 t - 1, y = 2 t + 4, z = 5 - t Determine whether the point ever reaches the position (8, - 2, 1) . If so, find the value of t .

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Question 3

Does the line r (t) = (1, 0, 1) + t (8, 7, 2) pass through the point (17, 14, 5) ? If so, find the value of t .

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Question 4

Determine whether the trajectory defined by r (t) = (23) + t (5 - 2) passes through the point (17, - 1) . If it does, find the corresponding parameter t .

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Question 5

Does the parameterised curve r (t) = (2 cos t, 2 sin t) pass through (1, 1) ? If so, find t in the interval [0, 2 π) .

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Question 6

A cycloid is defined by the vector equation r (t) = (t - sin t, 1 - cos t) Does it pass through the point (π, 2) ? If so, find the value of t .

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Question 7

Does the circle parameterised by r (t) = (3 cos t, 3 sin t) pass through (- \frac{3}{2}, \frac{3 3}{2}) ? Find t .

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Question 8

Determine whether the trajectories r_{1} (t) = 100 + t 234 and r_{2} (s) = - 1 42 + s 3 - 1 2 intersect. If so, find the values of t and s and the point of intersection.

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Question 9

The line L passes through the points A (1, 2, 3) and B (4, 5, 6) . The vector equation of L is given by r = O A + t A B, where t is a scalar parameter. Find the value of t for which the point C (7, 8, 9) lies on L .

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Question 10

A projectile’s position is given by r (t) = (0, 0, 0) + t (5, 10, 0) + t^{2} (0, - 5, 0) Does it pass through (10, 5, 0) ? If yes, find t .

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Question 11

Does the helix r (t) = (cos t, sin t, t) pass through the point (\frac{1}{2}, \frac{3}{2}, \frac{π}{3}) ? Find t if it does.

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IB Mathematics Applications & Interpretation Question Type 2: Determining with an Object Given a Trajectory Passes a Specific Point Exercises