1. ## Difficult Projectile Question

Question:

"a golfer hits a ball 135 metres on flat ground, 5m before it hits the ground it is at 1.8m high. Calculate the initial velocity"

Any help?

Nick

p.s. ignoring air resistance and all the usual stuff g=9.8m/s2

2. ## Re: Difficult Projectile Question

Originally Posted by Nicholasnewport
Question:

"a golfer hits a ball 135 metres on flat ground, 5m before it hits the ground it is at 1.8m high. Calculate the initial velocity"

Any help?

Nick

p.s. ignoring air resistance and all the usual stuff g=9.8m/s2
$\noindent Let the initial speed be V and angle of launch \theta \Big{(}which is an angle between 0^{\circ} and 90^{\circ}, i.e. between 0 and \frac{\pi}{2} in radians\Big{)}. Assume the launch occurs from the origin (where x = 0 and y = 0) as usual. By symmetry of parabolic flight, we equivalently have that the height is y = 1.8 at distance 5 metres from the launching place (where x = 5).$

$\noindent The range R of the projectile is given by R = \frac{V^{2} \sin 2\theta}{g} (see a Wikipedia link below). We know that this is 135, so we have$

$\boxed{\frac{V^{2} \sin 2\theta}{g} = 135. \quad (1)}$

$\noindent Now, we also know that y = 1.8 when x = 5. We know (see a Wikipedia link below) that the projectile's trajectory y in terms of x is given by$

$y = x \tan \theta - \frac{gx^{2}}{2V^{2}\cos^{2} \theta}.$

$\noindent So substituting x = 5 and y = 1.8 into this gives us$

$\boxed{5\tan \theta - \frac{25g}{2V^{2} \cos^{2} \theta} = 1.8. \quad (2)}$

$\noindent We thus have two equations in two unknowns (V and \theta), which we can solve to find the initial velocity, so you can have a go at solving these now \Big{(}remember V > 0 and 0 < \theta < \frac{\pi}{2}\Big{)}.$

$\noindent \textbf{Note.} For exam purposes, you will need to derive the equations I quoted above (shown in the Wikipedia links below), rather than just quote them. They are standard derivations that you should know how to do.$

$\noindent Links:$

- Range of projectile: https://en.wikipedia.org/wiki/Trajec...tance_traveled
- Trajectory equation (with y0 = 0): https://en.wikipedia.org/wiki/Trajec...le#Height_at_x .

3. ## Re: Difficult Projectile Question

As unhelpful as this is, the question appears to be outside the scope of the HSC physics course. Especially for prelim...

4. ## Re: Difficult Projectile Question

Originally Posted by mattskioner
As unhelpful as this is, the question appears to be outside the scope of the HSC physics course. Especially for prelim...
It's from within the HSC maths syllabus (3U Projectile motion probably).

5. ## Re: Difficult Projectile Question

Originally Posted by InteGrand
It's from within the HSC maths syllabus (3U Projectile motion probably).
I think it shouldn't be in the prelim forum, projectile motion is HSC in both 3u and physics.

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