Could you please reply to the following once you're free? It seems you're already busy in two rooms.
> In projectile motion, the modulus of rate of change of speed:
> (a) is constant
> (b) first increases then decreases
> (c) first decreases then increases
> (d) None of the above
My approach:
I decomposed the two dimensional motion to two orthogonal one dimensional motions - one along the horizontal and the other vertical. I'm calling the horizontal axis as the $x$ axis and the vertical as the $y$ axis.
The acceleration along the $x$ axis is zero whereas it's $g$ along the $y$ axis. So the velocity remains constant along the $x$ but it changes along the $y$ axis.
The speed of the projectile during the ascending phase decreases with time and it increases when it starts its descending phase. So rate of change of speed is $-g$ for half the flight time and $+g$ for the remaining half.
As the question asks for the modulus of rate of change of speed, the answer is always $g$. Or as per the options, the modulus of rate of change of speed remains constant (option a).
But the book states the answer to be (c). Could you please tell whether the answer in the book is incorrect or not?
Ok sir. If possible, can you please look at the previous block of messages? That's a simple question from kinematics however I'm facing issues with the answer provided by the book.
I don't know exactly what shape the curve is because I'd need to differentiate the equation for $u$ to get that, but we know it starts off positive, goes to zero then goes positive again. So it's going to look something like this. Yes?
And the question asks about "modulus of rate of change of speed" i.e. $|du/dt|$
I think we can also express the same thing as: $$\frac{du}{dt}=g\sin\theta$$ where $\theta$ is the angle between the velocity vector and the horizontal.
That is certainly not going to look like a graph of $|x|$, shifted or otherwise.
@JohnRennie: I agree with this point. But is that because of the constant horizontal component of the velocity which causes the variation from a linear graph?
Ok sir. So even though one of the components of velocity has a linear relation and the other orthogonal component remains constant, the resultant velocity may not have a linear relation. I didn't realise this so far. Could you please tell whether this conclusion is correct or not, sir?
