Projectiles – Starting From Above or Below y=0

If a particle is projected from a point above ground level, we can take this into account by changing the datum, so that it becomes the point of projection. For example, if a particle is projected from a point 2m above the ground then we can take this into account by takingas the point 2m above ground level, so the ground becomes

Example:

A ball is projected vertically upwards from a height of 5 metres above ground level. Its initial speed is 7 m/s . Assume that the ball is a particle and that no resistance forces act on it as it moves.

(a) Show that the maximum height of the ball is 7.5 metres above ground level.

(b) Show that the time that it takes the ball to reach its maximum height is 0.714 seconds, correct to three significant figures.

(c) The ball is caught when it is at a height of 2 metres above ground level.

(i) Find the total time for which the ball is moving.

(ii)Find the speed of the ball when it is caught.

(a)

(b)

to 3sf.

(c)(i)

to 2 dp.

Sincecannot be negative, which would mean arriving before departing,to 2 dp.