# Does this kinematics problem involve rotational motion?

I'm given the following problem:

A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 30 ∘ above the horizontal. Top-rated javelin throwers do throw at about a 30 ∘ angle, not the 45 ∘ you might have expected, because the biomechanics of the arm allow them to throw the javelin much faster at 30 ∘ than they would be able to at 45 ∘ . In this throw, the javelin hits the ground 57 m away. (To clarify, the problem is asking you for the acceleration provided by the thrower herself, not the acceleration of the javelin once it is in the air (where the acceleration would of course be -$$g$$)

I'm not entirely sure how to approach this. Here's my thinking:

We know that the javelin must stay in the air long enough to travel $$57m$$. So, if we break this two-dimensional motion into two components:

$$y = y_0 + v_{y0}t + 1/2 a_yt^2$$

$$x = x_0 + v_{x0} + 1/2a_xt^2$$

Perhaps somehow we can determine a velocity, and from that somehow determine what acceleration would be needed to bring the javelin from $$v_0 = 0$$ to whatever that velocity may be.

Is this the right way to think about this? Is there a better way? Is rotational motion involved (in the throw)? Where do I go from here?

(EDIT): Perhaps I could rotate the coordinate axis to "align" with that 30 degree angle, and then suppose that the 70cm traveled was in a straight line, and then compute the acceleration along that line (although, I'm still missing information).

• You are definitely overthinking this, it's just a standard projectile motion problem, you could replace the javelin with a ball and it'd be the same problem. Commented Oct 14, 2020 at 0:32
• Note that the "30 degrees" tells you the relationship between vx0 and vy0; there aren't 2 independent variables there.
– Luke
Commented Oct 14, 2020 at 1:12
• When the javelin is in the air, $a_x$ is zero (assuming x is horizontal). Commented Oct 14, 2020 at 16:55

First you need to work out the initial velocity of a projectile (the fact that it is a javelin is irrelevant) so that, released at an angle of $$30^o$$ and a height of $$2$$ m, it travels $$57$$ m before hitting the ground.
Once you have this initial velocity then you can work out the acceleration required to reach this velocity in a distance of $$0.7$$ m starting from rest. In this part you will have to assume a constant rate of acceleration. This is not necessarily realistic, but you are not given enough information to do anything else.