CPM Homework Help : PC3 Problem 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?

Step 1:

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

Step 2:

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

Step 3:

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

Step 4:

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