After how many seconds the ball will hit the ground can be determined by setting h (height) equal to zero:
0 = -16t^2 + 46t + 6
Rearranging the terms, we get:
16t^2 - 46t - 6 = 0
Now we can solve for t by factoring, using the quadratic formula or by completing the square. In this case, let's use the quadratic formula:
t = (-(-46) ± √((-46)^2 - 4*16*(-6))) / 2*16
t = (46 ± √(46^2 + 384)) / 32
t = (46 ± √(2116 + 384)) / 32
t = (46 ± √2500) / 32
t = (46 ± 50) / 32
This gives us two possible solutions for t:
t = (46 + 50) / 32 = 3.5 seconds
t = (46 - 50) / 32 = -0.125 seconds
Since time cannot be negative, the ball will hit the ground in approximately 3.5 seconds.
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=-16t^2+46t+6. After how many seconds will the ball hit the ground?
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