SHM and projectile problems- help needed (1 Viewer)

[xxmissy]

Hey guys I need help with these ... or how i would approach it:

Simple harmonic motion:

The period of a particle in moving in SHM in 6 s and its amplitude is 8cm. Calculate its velocity and acceleration (correct to 1 decimal place) when the displacement is 5cm from the centre of the motion.


Projectiles:

A horizontal drainpipe 6m above sea level empties stormwater into the sea. It the water comes out horizontally and reaches the sea 2m out from the pipe, find the initial velocity of the water, correct to 1 decimal place. Let g be 10m/s^2 and neglect air resistence.

Help would be very much appreciated!!

 

[watatank]

Projectiles:

A horizontal drainpipe 6m above sea level empties stormwater into the sea. It the water comes out horizontally and reaches the sea 2m out from the pipe, find the initial velocity of the water, correct to 1 decimal place. Let g be 10m/s^2 and neglect air resistence.

Help would be very much appreciated!!

i cant remember the variables they use in maths ext 1 or the methods used but i can tell you the physics method...hopefully you can follow...

let u = initial, v = final velocity, y = displacement in vertical direction, x = displacement in vertical direction, a = acceleration, t = time.

ok you need to find time.

consider the y direction first.

y = ut + 0.5at^2

u = 0, so y = 0.5at^2

solve for t, uve got height and acceleration due to gravity so plug them in and you got t.

t = sqrt(2y/a)

now consider the x direction.

you should know that

x = ut + 0.5at^2 ----> x = ut, since a = 0 in the x direction

uve got x, youve got t, so solve for u and thats ur intial velocity

sorry its kinda cluttered, hope you followed that.

 

[xxmissy]

thanx for that!!=)

 

[elseany]

For the first question:

Period:
2(pi)/n = 6
n = (pi)/3
a = 8

we can use the following formula; v² = n²(a² - x²)
substitute in our values for n and a and let x = 5

we get v² = 13(pi)²/2
so v = 6.5cm/s

for the second part you use the formula; x'' = -n²x
so just again sub in our value for n and x=5
and u should get x'' = a = -5(pi)²/9
so a = -5.5cm/s/s