A. A bowling ball is dropped from a height of 35 feet write a function that gives the height h (in feet) of the bowling ball after t seconds H(t)=__

B. Find the height of the bowling ball after 1 second

C. How long does the bowling ball take to hit the ground round your answer to the nearest hundredth of a second

Show all your work please and no cheating

See previous post: Wed, 3-2-16, 10:20 PM.

To solve these problems, we need to apply the laws of physics to the motion of the bowling ball. In this case, we can use the equation for the height of an object in free fall:

h(t) = h₀ + v₀t + (1/2)gt²

Where:
- h(t) is the height of the object at time t,
- h₀ is the initial height of the object,
- v₀ is the initial velocity of the object,
- g is the acceleration due to gravity,
- t is the time elapsed.

In our case:
- The initial height h₀ is 35 feet since the bowling ball is dropped from a height of 35 feet.
- The initial velocity v₀ is 0 feet/second since the bowling ball is initially at rest.
- The acceleration due to gravity g is approximately 32.2 feet/second².

Now let's solve each part of the problem:

A. The height of the bowling ball after t seconds is given by:

H(t) = 35 + 0t + (1/2)32.2t²
= 35 + 16.1t²

B. To find the height of the bowling ball after 1 second, substitute t = 1 into the equation:

H(1) = 35 + 16.1(1)²
= 35 + 16.1
= 51.1 feet

Therefore, the height of the bowling ball after 1 second is 51.1 feet.

C. To find how long it takes for the bowling ball to hit the ground, we need to find the time when the height h(t) becomes 0. Set h(t) = 0 and solve for t:

0 = 35 + 16.1t²
16.1t² = -35
t² = -35/16.1
t = √(-35/16.1) (taking the positive square root)

Since the square root of a negative number yields an imaginary result, it tells us that the ball will not hit the ground in our scenario. It indicates that the equation does not have a real solution for t when the height is zero.

Therefore, the bowling ball will not hit the ground in this setup.

Please note that in real-life situations, factors like air resistance and other variables may affect the ball's trajectory, making it eventually hit the ground.