A ball is thrown from an initial height of 2 meters with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following. h=2+13t-5t^2.

Question

Find all values of t for which the ball's height is 7 meters. Round your answer(s) to the nearest hundredth.

Answer 1

In this problem, we are given the function representing the ball's height in meters after t seconds, and are asked to find t when the height is equal to 7 meters. Since the variable h in the equation represents height, we can plug in 7 for h and solve for t.

2+13t-5t²=7

Let's put this into the standard form of a quadratic function: ax²+bx+c=0

This means that we have to move the 7 to the other side to make the right side equal to 0 (subtract by 7 on both sides).

-5t²+13t-5=0

It is implied by the problem that we must use the quadratic formula since our answers will not be whole numbers.

Plugging this function into the quadratic formula gives us:

(-13±√(13²-4(-5)(-5))) / 2(-5)

Now, simplify.

(-13±√69) / (-10)

Insert this into your calculator.

We get t ≈ 0.47 and t ≈ 2.13. We can use both these answers because they are both positive. Hope this helps!