a ball is thrown into the air with an initial upward velocity of 46 ft/s. its height (h) in feet after t seconds is given by the function h=-16t2+46t+6. after how many second will the ball hit the ground
a ) 3
b ) 4
c ) 5
d ) 6
To find when the ball hits the ground, we need to determine when the height (h) is equal to zero.
The equation for the height of the ball is given as h = -16t^2 + 46t + 6.
Setting h equal to zero, we get:
0 = -16t^2 + 46t + 6.
To solve this quadratic equation, we can use factoring, completing the square, or using the quadratic formula. In this case, factoring is the most convenient method.
Factoring the equation, we get:
0 = (2t + 1)(-8t + 6).
Setting each factor equal to zero, we have:
2t + 1 = 0 and -8t + 6 = 0.
Solving each equation, we find:
2t = -1 --> t = -1/2
-8t = -6 --> t = 3/4
We discard the negative solution as time cannot be negative in this context and choose the positive solution.
Therefore, the ball will hit the ground after 3/4 seconds.
Answer: The correct option is (b) 4.