Question

A ball thrown upwards hits a roof and returns back to the ground. the upward movement is modeled by a function s=−t²+3t+4 and the downward movement is modeled by s=−t²+3t+4 , where s is the distance (in metres) from the ground and t is the time in seconds. find the height of the roof from the ground. give your answer as a number without units.

Answer 1

The height of the roof is 4.25.

Step-by-step explanation:

The height of the roof can be determined by finding the maximum point of the upward movement function. The equation for the upward movement is s = -t² + 3t + 4. To find the maximum point, we can use the vertex formula, t = -b/2a, where a, b, and c are the coefficients of the quadratic equation. Plugging in the values, we get t = -3/(-2) = 1.5 seconds. Then, substitute this value into the equation to find the height: s = -(1.5)² + 3(1.5) + 4 = 4.25.