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) = 96t − 16t2 . Its horizontal displacement in feet is given by x(t) =96t. 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 = 96t – 16t2.
The velocity vector when t = 0 is:
Sketch this vector and use the Pythagorean Theorem to determine its magnitude.