Q3s

2001

2009

(a)

A straight vertical cliff is 200 m high. A particle is projected from the top of the cliff.

The speed of projection is 14 (10)^½ m/s at an angle 􀀁 to the horizontal.

The particle strikes the level ground at a distance of 200 m from the foot of the cliff.

(i) Find, in terms of 􀀁 , the time taken for the particle to hit the ground.

(ii) Show that the two possible directions of projection are at right angles to each other.

(b) A plane is inclined at an angle 60􀀉 to the horizontal.

A particle is projected up

the plane with initial speed u at an angle 􀀆 to the inclined plane.

The plane of projection is vertical and contains the line of greatest slope.

The particle strikes the plane at right angles.

Show that the range on the inclined plane is

g

u

13

4 3 2

.

Sx = 200 =

Rearrange for t .... (5)

(ii)

Sy = -200 = (5)

Sub in t ...... (5)

Find equation in terms of Tan

Tan 1 x Tan 2 = -1 => perpendicular (5)

Rj = 0 (5)

get an equation in t (5)

if it hits at right angle means Vi = 0

this leads to another equation in t (5)

Compare equations (5)

Find the Range (5)

Get a value (5)

2008