Answer: When the ball strikes the ground, its height above the ground is zero. So we can set h = 0 in the equation and solve for t:
0 = -16t^2 - 20t + 200
Dividing both sides by -4 (to simplify the equation):
0 = 4t^2 + 5t - 50
Now, we can use the quadratic formula to solve for t:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = 5, and c = -50.
t = (-5 ± sqrt(5^2 - 4(4)(-50))) / 2(4)
t = (-5 ± sqrt(625)) / 8
t = (-5 ± 25) / 8
So the two possible solutions are:
t = 3/2 or t = -5
Since time cannot be negative, the only valid solution is t = 3/2.
Therefore, the ball will strike the ground 1.5 seconds after it is thrown.
Explanation: