EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of a building, 350 m above the ground. (a) What is the velocity of the ball after 3 seconds? (b) How fast is the ball traveling when it hits the ground? SOLUTION We will need to find the velocity both when t = 3 and when the ball hits the ground, so it's efficient to start by finding the velocity at a general time t=a. Using the equation of motion s = f(t) = 4.9t², we have v(a) = lim f(a+h)-f(a) h→0 h = lim = lim = lim 4.9 h 4.9(a² + 2ah + h² − a²) h =lim 4.9 h→0 (a) The velocity after 3 s is v(3) = 9.8 h and / 350 t₁ = √√4.9 (b) Since the observation deck is 350 m above the ground, the ball will hit the ground at the time t₁ when s(t₁) = 350, that is, 4.9t₁2 = 350. This gives the following. (Round your approximation to one decimal place.) t₁² = 350 4.9 4.9a² m/s. m/s The velocity of the ball as it hits the ground is the following. (Round your answer to the nearest integer.) 350 v(t₁) = 9.8t₁ = 9.8 4.9