Question

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15/ms . The ball's height h (in meters) after t seconds is given by the following. =h+2−15t5t2 Find all values of t for which the ball's height is 7 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Answer 1

The height that a ball reaches at a certain time t is given by the equation,
           h = 2 - 15t + 5t²
We are asked to compute for the values of t that would allow the ball to reach a height of 7 meters. 

Substitute the 7 to the equation,
         7 = 2 - 15t + 5t²
Transposing,
               5t² - 15t - 7 + 2 = 0
Simplifying,
               5t² - 15t - 5 = 0
Divide the equation by 5,
               t² - 3t - 1 = 0

The values of t can be calculated through the quadratic formula,
             t = (-b +/- sqrt(b² - 4ac))/2a

Substituting, 
             t = (3 +/-sqrt (9 - 4(-1)) / 2(1)
              t = 3.3 or t = -0.30

Since, we cannot have t as a negative number hence, our final answer is:
       t = 3.3 s