A baseball is hit with an initial upward velocity of 70 feet per second from a height of 4 feet above the ground. The equation h
= −16t^2 +70t + 4 models the height in feet t seconds after it is hit. After the ball gets to its maximum height, it comes down and is caught by another player at a height of 6 feet above the ground. About how long after it was hit does it get caught?
To solve you need to set the equation equal to 6 (the height at which the player caught the ball.
6 = -16t^2 + 70t + 4
Next put the equation in standard form by subtracting 6 from both sides
-16t^2 + 70t - 2 = 0
This equation can be simplified by dividing by 2
-8t^2 + 35t - 1 = 0
This equation cannot be factored, but we can use the quadratic formula to find a value for x. Using the equation above we can find the values for a=-8, b = 35 and c = -1.
