Further Mathematics Notes

Motion Under Gravity In Two Dimension, Derivation And Application Of Equations Involving Greatest Height, Time Of Flight And Range

Motion Under Gravity in Two Dimensions:

If a particle is projected with an initial velocity u at angle θ to the horizontal, the prativle will be resolved into vertical and horizontal components of the velocity.


Calculations and Examples

EVALUATION: A  particle is projected into the air with a speed of 50m/s at an inclination sin-1(3/5). Find the: (greatest height reached by the particles; (ii) horizontal range; (iii) time of flight

Reading Assignment

New Further Maths Project 2 page 262 -270.


1) A particle is projected with an initial speed of 45m/s at an angle of 35 to the horizontal, find the time it takes for the particle to (i) reach the highest level (ii) return to its original level

2) A particle is projected horizontally with a velocity of 40m/s from the top of a tower 80.5m above the level ground  find how far from the bottom of the tower the particle when it hits the ground

3) A particle is projected into the air with a speed of 20m/s at an inclination 30 to the horizontal , find the (i) greatest height reached  (ii) horizontal range  (iii) time of flight

4) Show that a particle which is projected with a given velocity reaches its maximum range at an elevation of sin-1 (21/2 /2)


The vertical and horizontal components of the initial velocity of a projectile are 36m/s and 64m/s respectively find the

1) greatest height reached  a) 32.4m  b) 97.2m  c) 64.8m  d) 16.2m

2) time of flight a) 7.2s   b) 3.6s  c) 1.8s  d) 14.4s

3) horizontal range  a) 23.04m  b) 46.08m  c) 11.5m  d) 92.16m

4) initial velocity of the projectile  a) 73.4m/s  b) 146.8m/s  c) 36.7m/s  d)18.4m/s

5) inclination to the horizontal  a) 19  b) 21  c) 29  d) 49


1) Find the initial speed which a projectile must be subjected to give a maximum horizontal range of 490m

2) Prove that the maximum range on a horizontal plane of a particle fired with velocity V at an angle x to the horizontal is V2 / g

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