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 = ?.