Problema Solution
At 9:45 Pete threw a ball upwards while standing on a 75 ft. platform. The trajectory after t seconds follows the equation: h(t)=-0.3t^2+60t+75.
What will be the balls max height?
How long will it take for the ball to reach max height?
At what time will the ball hit the ground?
Answer provided by our tutors
h(t)=-0.3t^2+60t+75
What will be the balls max height?
We need to find the maximum value of the parabolic function h(t)=-0.3t^2+60t+75
since the quotient infron of t^2 is negative: -0.3 < 0 the function has maximum equal to
h max = c - (b^2)/(4a) where a=-0.3, b=60 and c=75
h max = 75 - (60^2)/(4*(-0.3))
h max = 3,075 ft
How long will it take for the ball to reach max height?
For h = 3,075 ft we need to find t
-0.3t^2+60t+75 = 3075
-0.3t^2+60t-3000 = 0 divide both sides by -0.3
t^2 - 200t + 10000 = 0
by solving we find
t = 100 sec
click here to see the step by step solution of the quadratic equation
At what time will the ball hit the ground?
It will hit the ground when h(t)=0 for some t<>0
-0.3t^2+60t+75=0
by solving we find
t = 201.24 sec
click here to see the step by step solution of the equation
201.24/60 = 3.354 min or 3 min 31 sec approximately
9:45 + 3 min 21 sec = 9:48:21
the ball will hit the ground at 9:48:21.