### Home > APCALC > Chapter 11 > Lesson 11.4.1 > Problem11-111

11-111.

A projectile travels through the air with position $x\left(t\right) = 15t$ and $y\left(t\right)=-4.9t^2+46t+11$ where $x$ is horizontal displacement and $y$ is height above the ground where both are measured in meters and $t$ is in seconds.

1. When does the projectile hit the ground?

When does $y = 0$?

2. How far does the projectile travel during its trip through the air? That is, calculate the length of the path of the projectile.

$\int_0^{9.621}\sqrt{(x^\prime(t)^2+(y^\prime(t)^2}dt$

3. What is the maximum height of the projectile?

This is when $y′ = 0$.

4. What are the acceleration and velocity vectors of the projectile at time $t = 2$ seconds?

$\vec{v}(2)=\langle x^\prime(2),y^\prime(2)\rangle$