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) a
fter 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.)
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: <em> t = 3.3 s</em>
