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
