Question

a ball is thrown into the air with a velocity of 36 ft/s. its height, in feet, after t seconds is given by s(t) = 36t − 16t2. find the velocity (in ft/s) of the ball at time t = 1 second.

Answer 1

The velocity of the ball at time t = 1 second is calculated by differentiating the height function s(t) to obtain the velocity function v(t), and then substituting t = 1 into this function to get 4 ft/s.

Step-by-step explanation:

To find the velocity of the ball at time t = 1 second, we need to differentiate the height function s(t) with respect to time t, which gives us the velocity function v(t). The height function provided is s(t) = 36t - 16t2. Differentiating, we get v(t) = ds/dt = 36 - 32t. Substituting t = 1 into the velocity function, we get v(1) = 36 - 32(1) = 4 ft/s. Therefore, the velocity of the ball at 1 second is 4 ft/s.