Edexcel A-Level Mathematics AS M1.2.1 Magnitude and Direction Questions

Practise combining i and j components, finding resultant magnitudes and bearings, choosing quadrants, and solving unknown force components from local M1 evidence.

Exam points

calculate a resultant vector by collecting i and j components before using Pythagoras
find bearings or angles from component differences, choosing the correct quadrant
use a vector diagram or components to solve for an unknown force magnitude

[Maximum number: 5]

[In this question i and j are horizontal unit vectors directed due east and due north respectively.]

A particle P moves with constant acceleration $(-\lambda \mathbf{i}+2 \lambda \mathbf{j}) \mathrm{ms}^{-2}$ , where $\lambda$ is a positive constant.

At time t=0, the velocity of P is $(5 \mathbf{i}-8 \mathbf{j}) \mathrm{m} \mathrm{s}^{-1}$

Find the direction of motion of P when $t=4 \mathrm{~s}$ , giving your answer as a bearing to the nearest degree.

( -2 i+4 j ) seen or implied
(5 i-8 j)+(-2 i+4 j) 4

Figure for Answer to Question Edexcel A-Level Mathematics AS M1.2.1 Magnitude and Direction Questions question 1 — Edexcel A-Level Mathematics AS

$339^{\circ}$
(5)

(10)

Notes for question 4

(a)
Or column vector

Complete method to find the velocity when t=4.

Correct unsimplified expression. Note the correct velocity is v=-3 i+8 j

Use their velocity vector at t=4 with trig to find a relevant angle.

Cao. Degrees sign not required.

N.B. if they work with both values of $\lambda$ , can score max all the marks except the last one.

QUESTION
NUMBER

SCHEME

MARKS

5

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Edexcel A-Level Mathematics AS M1.2.1 Magnitude and Direction Questions question 1