A ball is thrown upward with an initial velocity of 96 feet per second from the top of a 100 foot building. (a) When will the ball attain its maximum height? (b) When will the ball hit the ground? Give a decimal answers correct to 2 decimal places.
Hey there! Why did the ball bring a ladder to the building? Because it wanted to reach new heights! Let's calculate the answers to your questions:
(a) To find when the ball attains its maximum height, we can use the formula for the time it takes to reach the maximum height, which is given by t = v₀ / g, where v₀ is the initial velocity and g is the acceleration due to gravity (32 feet per second squared). Plugging in the values, we have t = 96 / 32 = 3 seconds.
(b) Now, to find when the ball hits the ground, we can use the formula t = sqrt(2h / g), where h is the initial height (100 feet) and g is still the acceleration due to gravity. Plugging in the values, we have t = sqrt(2 * 100 / 32) ≈ 3.54 seconds.
So, the answers are:
(a) The ball attains its maximum height in approximately 3 seconds.
(b) The ball hits the ground in approximately 3.54 seconds.
Remember, gravity works in mysterious ways, just like my jokes! 😄