Question

The height of a rock is thrown from a 50 meter cliff is given by h(t)=-4.9t^2 9t 50 where t is time in seconds after being thrown. At what time will the rock return to a height of 50 meters

Answer 1

The rock will return to a height of 50 meters at t = 2.25 seconds.

Step-by-step explanation:

To find the time at which the rock returns to a height of 50 meters, we can set the height function h(t) equal to 50 and solve for t. The height function is given by h(t) = -4.9t^2 + 9t + 50.

So, we have the equation -4.9t^2 + 9t + 50 = 50. Simplifying this equation, we get -4.9t^2 + 9t = 0.

Rearranging, we have t(-4.9t + 9) = 0. This gives us two possible solutions: t = 0 and t = 9/4 = 2.25 seconds.

Since time cannot be negative, the rock returns to a height of 50 meters at t = 2.25 seconds.