0= -4.9t^2+24t+3000

solve for t

Use the quadratic equation

27.31348

To solve the equation 0 = -4.9t^2 + 24t + 3000 for t, we can use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

In our equation, a = -4.9, b = 24, and c = 3000. Plugging these values into the quadratic formula gives us:

t = (-24 +/- sqrt(24^2 - 4(-4.9)(3000))) / 2(-4.9)

Simplifying the equation further yields:

t = (-24 +/- sqrt(576 + 58800)) / -9.8

t = (-24 +/- sqrt(59376)) / -9.8

Now, let's find the square root of 59376:

t = (-24 +/- 243.52) / -9.8

Now we can proceed to find the two solutions for t by adding and subtracting 243.52 from -24:

Solution 1: t = (-24 + 243.52) / -9.8 = 219.52 / -9.8 = -22.41

Solution 2: t = (-24 - 243.52) / -9.8 = -267.52 / -9.8 = 27.34

Therefore, the solutions for t in the equation 0 = -4.9t^2 + 24t + 3000 are t = -22.41 and t = 27.34.