College Algebra

Question

A ball is thrown vertically upward from the top of a building 800 feet tall with an initial velocity of 80 feet per second. The distance d (in feet) of the ball from the ground after t seconds is d(t)= 800 + 80t - 16t^2. What is the maximum height of the ball? After how many seconds will the ball hit the ground?

Answer 1

d(t) = -16t² + 80t + 800

Maximum height is at the vertex of the height-vs.-time parabola, which is at

t = -80/[2(-16)] sec = ? sec

Evaluate d(t) at this value of t to get maximum height. To find the time to reach the ground, set d(t)=0 and solve the resulting quadratic equation using the quadratic formula. You will get a positive and a negative solution. Since time starts at t=0, the positive solution is the correct one.