If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = - 16t2 + 64t + 4. 2 plus or minus square root of 17 end root over 2 quantity of 2 plus or minus square root of 17 all over 2 2 plus or minus 4 square root of 17 quantity of 16 plus or minus square root of 17 all over 2

This is the concept of trajectories;

We are required to calculate the time taken for the base ball whose distant to reach the maximum height has been modeled by h=-16t^2+64t+4.2 took to hit the ground. Here we proceed as follows;

At the time when the base ball hits the ground the height, h=0

Thus;

-16t^2+64t+4.2=0

this is a quadratic equation, to solve the quadratic equation we use the formula;

t=[-b + / - sqrt (b^2-4ac) ] / (2a)

where;

a=-16, b=64, c=4.2

thus substituting the values in our formula we get:

t=[-64+/-sqrt (64^2-4 * (-16) * 4.2) ] / (-16*2)

t=[-64 + / - sqrt (4364.8) ] / (-32)

t=[-64+/-66.1] / (-32)

t=4.1 or-0.1

thus the we take the positive value t=4.1 and we conclude that the time taken for the ball to hit the ground was 4.1 seconds