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  • Projectile Motion Problem: Calculating Horizontal Range of a Football Pass
    We have:

    $$\overrightarrow v_i=v_i\cos\theta\hat{i}+v_i\sin\theta\hat{j}=(25\cos35\degree)\hat{i}+(25\sin35\degree)\hat{j},$$

    $$t=2.55\text{ s},$$

    $$y_f=0,$$

    $$a_y=-g=-9.8\text{ m/s}^2.$$

    The range (horizontal distance) is:

    $$x_f=x_i+v_{xi}t=\left[(25\cos35\degree)(2.55\text{ s})\right]\hat{i}=\boxed{49.3\text{ m}}$$

    The maximum height is:

    $$y_{max}=y_i+v_{yi}t+\frac{1}{2}a_yt^2=0+\left[(25\sin35\degree)(2.55\text{ s})\right]+\frac{1}{2}(-9.8\text{ m/s}^2)(2.55\text{ s})^2$$

    $$y_{max}=\boxed{16.3\text{ m}}$$

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