ANSWER
[tex]\begin{gathered} (a)\text{ }12.61\text{ }s \\ (b)\text{ }194.73m \\ (c)\text{ }608.57\text{ }m \\ (d)\text{ }78.4\text{ }m\/s \end{gathered}[/tex]EXPLANATION
Parameters given:
Initial velocity, v0 = 78.4
Angle of projectile, θ = 52 degrees
(a) To find the flight time of the tennis ball, apply the formula:
[tex]t=\frac{2v_0\sin\theta}{g}[/tex]where g = acceleration due to gravity
Hence, the total flight time of the tennis ball is:
[tex]\begin{gathered} t=\frac{2*78.4*\sin52}{9.8} \\ t=12.61\text{ }s \end{gathered}[/tex](b) To find the maximum altitude of the ball during its flight, apply the formula:
[tex]H=\frac{v_0^2\sin^2\theta}{2g}[/tex]Therefore, the maximum height attained by the tennis ball is:
[tex]\begin{gathered} H=\frac{78.4^2*\sin^2(52)}{2*9.8} \\ H=194.73\text{ }m \end{gathered}[/tex](c) To find the horizontal distance the tennis ball travels, apply the formula:
[tex]R=\frac{v_0^2\sin2\theta}{g}[/tex]Hence, the horizontal distance traveled by the tennis ball is:
[tex]\begin{gathered} R=\frac{78.4^2*\sin(2*52)}{9.8} \\ R=608.57\text{ }m \end{gathered}[/tex](d) To find the final velocity of the tennis ball, apply the formula:
[tex]v=\sqrt{v_0^2+2h(-g)}[/tex]where h = initial height = 0 m
Hence, the final velocity of the tennis ball just before impact is:
[tex]\begin{gathered} v=\sqrt{78.4^2+2(0)(-9.8)} \\ v=\sqrt{78.4^2+0}=\sqrt{78.4^2} \\ v=78.4\text{ }m\/s \end{gathered}[/tex]