you throw a ball upward at an initial velocity of 30 feet per second from 6 feet off the ground.

Question

After how many seconds and what height will the ball reach its maximum height? How many seconds until the ball hits the ground?

Answer 1

The mathematical for height above ground is s(t) = -½gt² +30t + 6;

the first term reflects the action of gravity (and g = 32 ft/sec²);

the second term shows distance traveled upward as a function of time (w/o gravity), and the

third term tells you initial height at time t=0.

 

The ball will attain its maximum height when t = -b/(2a), where a and b are the first two coefficients of the s(t) function--this is at the vertex since the function is a parabola opening in the downward direction. a=-16.

 

t= -30/[2(-16)] = 15/16 second.  To find maximum height, calculate s(15/16).

 

To find the time to come to earth, solve the equation s(t) = 0.