### Home > PC3 > Chapter 11 > Lesson 11.1.3 > Problem11-53

11-53.

In a baseball game, Alex hits a ball with an initial velocity of $110 \text{ ft/s}$ at an angle of $53º$ with the horizontal. The ball was struck at an initial height of $4$ feet. Alex will hit a homerun if the ball travels $330$ feet and has a height of at least $10$ feet. Does Alex hit a homerun? How far will the ball have traveled horizontally when it hits the ground?

Use parametric equations to solve this problem.
To determine when the ball will hit the ground, solve $y(t) = 0$.
Since the velocity is given in ft/s, use $−16 \text{ ft/s}^{2}$ for acceleration due to gravity.

$x(t) = (110\cos(53º))t$
$y(t) = −16t^2 + (110\sin(53º))t + 4$