A mistake in a physics SAT prep book or an Underlying Paradox in freefall explanation?! HELP NEEDED

Archive SAT Subject Test Preparation
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<p>In an SAT practice book, when the book wanted to explain a problem regarding freefall, it was something like this:</p>

<p>Let’s look at a problem where an object is thrown into the air and
returns.
A girl throws a baseball straight up and catches the ball
at the same height 2.6 seconds later. How fast did the girl
throw the ball into the air?</p>

<p>In the solution, the book assumed Vf to be 0 (which I wholly agree with) and used the formula "s = vi t + 0.5gt^2 "</p>

<p>When the book wanted to discuss a problem concerning CURVILINEAR MOTION it was something like this:</p>

<p>Consider a fisherman making a long cast. His lure is released as the
rod moves forward on the cast. The lure rises into the air while at the
same time moving forward across the water. The lure then falls to the
water as it reaches the fisherman’s target.
After careful observation, one can state the following information
about the fisherman’s cast (above): The lure always leaves the rod
tip (considered ground level) at an angle of 30° and a velocity of 22
m/s. How far does the fisherman cast his lure?</p>

<p>In the solution however, when they wanted to exclude Vy (which was calculated to be 11 m/s) and treat it as a freefall problem in its own to find the time taken, they did not take Vyfinal as “0” but rather as 11 m/s. Vyinitial as -11 m/s</p>

<p>and they found the time by (Vyfinal - Vyinitial)/ acceleration (linear motion equation rearranged)</p>

<p>Anyway so my question is, why did they take vyfinal as a value not as 0?! Is it a mistake? or is it?</p>

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<p>v<em>f should not be 0 at the end. That is an incorrect assumption. The first problem does not assume v</em>f to be 0. The equation used, s=(v<em>i)t+0.5gt^2 does not assume v</em>f is 0.</p>

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<p>For the first problem you can use vf = vi + at; here as the ball reaches its max height vf = 0, so you get vi = -at. ‘a’ here is acceleration and t is time so you get the value of vi as 9.8*1.8 = 17.64</p>

<p>For the 2nd problem, you can divide the velocity into 2 components, vertical and horizontal component.
The vertical component is equal to v<em>sin(30) = 11. So if you just consider the vertical component of the velocity the problem becomes like a free fall problem. Using this, find the time of flight of the lure which is ~1.12 seconds. Now, consider the horizontal component of the velocity. The distance covered would be s = ut + 0.5a(t^2), but acceleration in the horizontal direction is zero, so distance = v</em>cos(30) * 1.12 = ~ 21.388</p>