(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An athlete can throw a javelin 60m from a standing position. If he can run 100m at constant velocity in 10s, how far could he hope to throw the javelin while running? Neglect air resistance and the height of the thrower in the interest of simplicity.

2. Relevant equations

I've found the range to be R(θ) = 2 v0/g sinθ (v0 cosθ + vr)

where v0 is the initial velocity and vr is the velocity of the thrower's initial run.

3. The attempt at a solution

Given the above equation and the premise that the thrower can throw 60m from standing, I solved for v0 using vr=0, R=60, g=9.8, and θ=45° as that is the ideal throwing angle from standing. I found v0 = √(60g).

Next I tried to find the ideal angle to throw at when vr = 10 m/s. I did this by taking solving R'(θ)=0 where R'(θ) is the derivative of the range formula. I found:

R'(θ) = c v0²/2 cos2θ + c vr cosθ = 0 where c = 2 v0/g.

This yielded the equation v0 cos2θ = -vr cosθ. Using an identity for cos2θ, I obtained the following quadratic equation:

2 cos²θ + d cosθ -1 = 0 where d = vr/v0 = 10/√(60g).

Solving for θ I got θ = 0.65 rads = 37°. The book, however, lists 52.3° as the angle, and therefore gets a different value of R than I do. I'm not sure where I went wrong with my logic.

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# Homework Help: Throwing a Javelin (Projectile Motion)

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