### Home > CALC > Chapter 12 > Lesson 12.1.3 > Problem12-39

12-39.
1. A ball is thrown from a window 25 meters above the ground with an initial velocity of 40 meters per second and an angle of inclination of . Let the origin be the point on the (level) ground below the window. Homework Help ✎

1. Assume the acceleration due to gravity is −10 . Find x(t) and y(t).

2. Find the angle at which the ball hits the ground.

$\vec{v}(t)=\langle v_0\cos(\theta),v_0\sin(\theta)+a(t)\rangle=\langle 40\cos\Big(\frac{\pi}{6}\Big),40\sin\Big(\frac{\pi}{6}\Big)-10t\rangle$

$x(t)=40t\cos\Big(\frac{\pi}{6}\Big)+C_1\text{ }y(t)=40t\sin\Big(\frac{\pi}{6}\Big)-5t^2+C_2$

First, determine when the ball hits the ground. This is when y(t) = 0.

Then angle is the angle created by the slope.
Think of drawing a slope triangle and calculating the angle.