Question

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

Answer 1

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