Motion question (2 Viewers)

[Shuuya]

Question:

A ball is thrown into the air, and the height of the ball above the ground in metres after t seconds is given by the equation

x = 2e - t + 2log(t+1)

(i) Find when the ball comes to a rest.

_____________________________________________


I don't know if I'm being stupid but I can't seem to solve for t when x = 0 ;-;

 

[kawaiipotato]

The ball comes to a rest when the velocity equals zero. Letting x = 0 means you're finding the time where the ball started.

 

[KingOfActing]

Ball at rest -> ball isn't moving -> velocity is zero

so v(t) = x'(t) = 0

-1 + 2/(t+1) = 0 -> t = 1

 

[Shuuya]

I am stupid.

(thanks! xD)

 

[InteGrand]

Setting x = 0 and solving for t would give the time when x = 0 (of course), not in general the time when the ball started. (The time of starting is just t = 0 of course. In this Q., the ball starts at x = 2e.)

 

[Shuuya]

Setting x = 0 and solving for t would give the time when x = 0 (of course), not in general the time when the ball started. (The time of starting is just t = 0 of course. In this Q., the ball starts at x = 2e.)

I completely missed that bit haha.

I was thinking that x would be 0 initially and when the ball landed, so I tried solving for t, completely forgetting about velocity etc..

 

[eyeseeyou]

Is this projectile motion?

 

[Nailgun]

Is this projectile motion?

no, it's just regular motion

 

[eyeseeyou]

no, it's just regular motion

Theres 3 types of motion iirc: projectile, motion in a straight line and simple harmonic

 

[Nailgun]

Theres 3 types of motion iirc: projectile, motion in a straight line and simple harmonic

.

 

[leehuan]

We call essentially all of the motion taught to be under the category of rectilinear motion, which is motion along a straight line so to speak. We compare the motion of a particle to that of one point - the origin.

Simple harmonic motion is a special type of rectilinear motion and should never be distinguished from it. It is specifically motion exhibiting an oscillatory behaviour about a fixed point.

I will not state specifically that projectile motion is rectilinear out of doubt, but we analyse it the exact same way. The only difference is that projectile motion is analysed in two-dimensions, not one.

 

[Nailgun]

We call essentially all of the motion taught to be under the category of rectilinear motion, which is motion along a straight line so to speak. We compare the motion of a particle to that of one point - the origin.

Simple harmonic motion is a special type of rectilinear motion and should never be distinguished from it. It is specifically motion exhibiting an oscillatory behaviour about a fixed point.

I will not state specifically that projectile motion is rectilinear out of doubt, but we analyse it the exact same way. The only difference is that projectile motion is analysed in two-dimensions, not one.

3 dimensions
time is a dimension

 

[leehuan]

3 dimensions
time is a dimension

True.

But we do not choose to draw a t-axis in Ext 1 maths when we analyse projectile motion.

 

[InteGrand]

Rectilinear motion is motion along a straight line, so only one-dimensional motion. For projectile motion in the HSC, it's two-dimensional. (Referring to spatial dimensions.)

Further info and equations about rectilinear motion may be found here: https://en.wikipedia.org/wiki/Linear_motion .

Here's a more detailed page on the equations of motion: https://en.wikipedia.org/wiki/Equations_of_motion .

And here's the Wikipedia article about projectile motion, including lots of equations: https://en.wikipedia.org/wiki/Projectile_motion .

There's also lots of useful projectile formulas here: https://en.wikipedia.org/wiki/Trajectory_of_a_projectile .

(Of course in the HSC, you're not allowed to quote these formulas. So it would be better to use those Wikipedia pages' formulas as exercises of things to prove about projectile motion, and maybe keep in mind that there are such formulae, which may be useful at times.)