A soccer ball is kicked from the ground with an initial upward velocity of
90 feet per second. The equation h = -16f + 90t gives the height h of the
ball after t seconds.
a. Find the maximum height of the ball.
1a. -
b..
b. How many seconds will it take for the ball to reach the ground?
a. To find the maximum height of the ball, we need to find the vertex of the parabolic function h = -16t^2 + 90t.
The vertex of a parabola in the form ax^2 + bx + c is given by the formula x = -b/2a.
In this case, a = -16 and b = 90. Plugging these values into the formula, we get:
t = -90 / (2*(-16)) = -90 / (-32) = 2.8125 seconds
Now, to find the maximum height, we plug this value of t back into the equation:
h = -16(2.8125)^2 + 90(2.8125)
h ≈ 126.56 feet
Therefore, the maximum height of the ball is approximately 126.56 feet.
b. To find out how many seconds it will take for the ball to reach the ground, we need to set h = 0 and solve for t in the equation -16t^2 + 90t = 0.
-16t^2 + 90t = 0
-16t(t - 5.625) = 0
This equation will be true when either t = 0 or t = 5.625 seconds.
Therefore, it will take approximately 5.625 seconds for the ball to reach the ground.