1. velocity

hey i really need urgent help and i know this is a maths forum but i think this forum is really good. Its my physics homework on suvat equations and maths is closely associated with physics

I really dont get this question

1.A particle falls freely from a rest. In the last second of its motion, it falls 5/9 of its total fall. How far did it fall?

and

2. A ball is dropped from a height of 20m and rebounds with a velocity which is 3/4 of the verlocity with which it hits the ground. What is the time interval between the first and second bounces?

im really stuck, thanks ellie x

2. Originally Posted by mitchoboy
hey i really need urgent help and i know this is a maths forum but i think this forum is really good. Its my physics homework on suvat equations and maths is closely associated with physics

I really dont get this question

1.A particle falls freely from a rest. In the last second of its motion, it falls 5/9 of its total fall. How far did it fall?

[snip]
Let x1 be the total distance particle falls. Let t1 be the time taken to fall this distance. Then:

u = 0
a = g
t = t1
s = x

Substitute all this into an appropriate straight line motion formula to get equation 1.

If it falls 5/9 of total fall in last second, then it falls 4/9 of total fall in t1 - 1 seconds:

u = 0
a = g
t = t1 - 1
s = (4/9) x

Substitute all this into an appropriate straight line motion formula to get equation 2.

Solve equations (1) and (2) simultaneously for x and t1.

3. Originally Posted by mitchoboy
[snip]
2. A ball is dropped from a height of 20m and rebounds with a velocity which is 3/4 of the verlocity with which it hits the ground. What is the time interval between the first and second bounces?

im really stuck, thanks ellie x
Calculate the velocity at which the ball hits the ground:

u = 0
s = 20
a = g
v = ?

Use 3/4 of this v as the initial velocity for the upward motion after 1st bounce. Call this velocity u. Then:

u = u.
a = g.
v = -u (assuming no air resistance)
t = ?

Note that v = -u because:

1. Final speed at impact = initial speed
2. Final speed is down, initial speed is up. Hence the sign change.

Note that after second bounce, the speed is 3/4 of u.

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a ball is dropped from height of 20m and rebounds with a velocity which is 3/4 of the velocity

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