Question

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s. The ball's height h (in meters) after t seconds is given by the following

h=2+25t-5t²
Find all values of t for which the ball's height is 7 meters.
Round your answer(s) to the nearest hundredth.

Answer 1

To find the values of 't' for which the ball's height is 7 meters, we set the equation for height 'h' equal to 7 and solve for 't' using the quadratic formula. The solutions are approximately 3.79 seconds and 0.54 seconds.

Step-by-step explanation:

To find the values of t for which the ball's height is 7 meters, we need to set the equation for the height h equal to 7 and solve for t.

Given the equation h = 2 + 25t - 5t², we can rewrite it as -5t² + 25t + (2 - 7) = 0.

This simplifies to -5t² + 25t - 5 = 0.

Using the quadratic formula, we can solve for t. The solutions are approximately t = 3.79 and t = 0.54.

Therefore, the values of t for which the ball's height is 7 meters are approximately 3.79 seconds and 0.54 seconds.