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

1.48

A. To find a function that gives the height h (in feet) of the bowling ball after t seconds, we can use the equation of motion for free fall:

h(t) = h0 - (1/2)gt^2

where:
h(t) is the height of the object at time t,
h0 is the initial height (35 feet in this case),
g is the acceleration due to gravity (approximately 32.2 ft/s^2).

Using these values, the function will be:

H(t) = 35 - (1/2)(32.2)t^2

B. To find the height of the bowling ball after 1 second, we substitute t=1 into the function H(t):

H(1) = 35 - (1/2)(32.2)(1^2)
H(1) = 35 - (1/2)(32.2)
H(1) = 35 - 16.1
H(1) = 18.9 feet

Therefore, the height of the bowling ball after 1 second is 18.9 feet.

C. To find how long it takes for the bowling ball to hit the ground, we set h(t) to 0 and solve for t:

0 = 35 - (1/2)(32.2)t^2

Rearranging the equation:

(1/2)(32.2)t^2 = 35

t^2 = (35 * 2) / 32.2
t^2 = 2.173913043

Taking the square root of both sides:

t ≈ √2.173913043

t ≈ 1.47377134 seconds (rounded to the nearest hundredth of a second)

Therefore, the bowling ball takes approximately 1.47 seconds to hit the ground.

A. To write a function that gives the height of the bowling ball after t seconds, we can use the formula for freefall motion:

H(t) = initial height - (0.5 * acceleration due to gravity * t^2)

Given that the initial height is 35 feet, and the acceleration due to gravity is approximately 32.2 ft/s^2, the function becomes:

H(t) = 35 - 16.1 * t^2

B. To find the height of the bowling ball after 1 second, we replace t with 1 in the function:

H(1) = 35 - 16.1 * 1^2
H(1) = 35 - 16.1
H(1) = 18.9 feet

Therefore, the height of the bowling ball after 1 second is 18.9 feet.

C. To find how long it takes for the bowling ball to hit the ground, we set H(t) to 0 and solve for t:

0 = 35 - 16.1 * t^2

Rearranging the equation:

16.1 * t^2 = 35

Dividing both sides by 16.1:

t^2 = 2.17391

Taking the square root of both sides:

t ≈ √2.17391

t ≈ 1.474 seconds

Therefore, the bowling ball takes approximately 1.474 seconds to hit the ground, rounded to the nearest hundredth of a second.

a. h(t) = 0.5g*t^2.

b. h(1) = 16*1^2 = 16 Ft.

c. h = 0.5g*t^2.
h = 35 Ft., g = 32 Ft/s^2, t = ?.