### Home > PC3 > Chapter 11 > Lesson 11.2.3 > Problem11-120

11-120.

A ball is thrown from a height of $6.5$ feet, travels a horizontal distance of $120$ feet, and hits the ground after $2.5$ seconds. What was the initial velocity of the ball?

$x(t) = v_0\cos(\theta)t$
$y(t) = -16t^2+v_0\sin(t) +6.5$

$120 = 2.5v_0\cos(\theta)$
$0 = -16(2.5)^2 + 2.5v_0 \sin(\theta)+6.5$

Solve the first equation for $v_0\cos(θ)$ and the second equation for $v_0\sin(θ)$.

Divide the two equations from Step 3, resulting in an equation for either $\tan(θ)$ or $\cot(θ)$, which can be solved for $θ$.