Chapter 2, Problem 34P

A research group is using a drop test to measure the force of attenuation of a helmet liner they designed to reduce the occurrence of brain injuries for soldiers and athletes. The helmet attached to a weight is propelled downward with an initial velocity v_i of 3 m/s from an initial height of 30 m. The behaviour of the falling helmet is characterized by a quadratic equation $h\left(t\right)=30-3t-49t^2$

(a) Write the quadratic equation for time when the helmet and weight hit the ground. i.e., $h\left(t\right)=0$ m.

(b) Solve the quadratic equation for t obtained in part (a) by completing the square, and the quadratic formula.