Suppose a baseball is thrown vertically upward from the ground with an initial velocity of v₀ ft/s. The approximate height of the ball (in feet) above the ground after t seconds is given by s(t) = -16t² + v₀t.
With what velocity does the ball strike the ground?

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the velocity of the baseball when it strikes the ground. The height function is given by s(t) = -16t^2 + v_0t, where s(t) is the height at time t, and v_0 is the initial velocity.
2. Step 2: Determine when the ball hits the ground. The ball strikes the ground when its height s(t) is 0. Set the equation -16t^2 + v_0t = 0 and solve for t.
3. Step 3: Factor the equation -16t^2 + v_0t = 0 to find the time t when the ball hits the ground. This can be factored as t(-16t + v_0) = 0, giving solutions for t.
4. Step 4: Use the derivative to find the velocity. The velocity function v(t) is the derivative of the height function s(t). Differentiate s(t) = -16t^2 + v_0t to find v(t).
5. Step 5: Substitute the time when the ball hits the ground into the velocity function v(t) to find the velocity at that moment. This will give the velocity with which the ball strikes the ground.