The equation for this problem is
h(t) = -16t^2 + 150t + 30
When will the firework land if it does not explode?
find t when h=0
To find when the firework will land, we need to determine the value of "t" when the height, h(t), is equal to zero. In this case, the height equation is given by:
h(t) = -16t^2 + 150t + 30
To find when the firework will land, we set h(t) = 0 and solve for t. So, we have:
-16t^2 + 150t + 30 = 0
Now, we can solve this quadratic equation using the quadratic formula. The quadratic formula is:
t = (-b ± √(b^2 - 4ac)) / 2a
In our case, a = -16, b = 150, and c = 30. Substituting these values into the quadratic formula, we have:
t = (-150 ± √(150^2 - 4(-16)(30))) / (2(-16))
Simplifying this equation will give us the two possible values for "t". It is important to note that if both values of "t" are positive, it means that the firework launches, reaches its peak, and then lands twice. However, if one of the values is negative, we take only the positive value as the time at which the firework will land.