### Home > CALC > Chapter 12 > Lesson 12.2.1 > Problem 12-67

12-67.

A projectile is launched from the ground at a 45° angle with altitude (in feet after

*t*seconds) given by*y*(*t*) = 96*t*− 16*t*^{2}. Its horizontal displacement in feet is given by*x*(*t*) =96*t.*Homework Help ✎Find an expression for the velocity vector as a function of

*t.*Calculate the magnitude of the velocity vector at

*t*= 0 and at the moment when the projectile hits the ground. Make a conjecture about the speed with which projectiles return to earth.

To determine when the projectile hits the ground, solve 0 = 96*t* – 16*t*^{2}.

The velocity vector when *t* = 0 is:

Sketch this vector and use the Pythagorean Theorem to determine its magnitude.