Suppose an object is dropped from a height h0 above the ground. Then its height after t seconds is given by h = −16t 2 + h0, where h is measured in feet. Use this information to solve the problem.

A ball is dropped from the top of a building 59 ft tall. (Round your answers to three decimal places.)
(a) How long will it take to fall half the distance to ground level?
t = sec

(b) How long will it take to fall to ground level?
t = sec

ho=59

h=0

0=-16t^2+59
t= 1/4 sqrt (59)

(a) How long will it take to fall half the distance to ground level?

To find this, we need to find the time when the height is half of the distance to ground level.

Half the distance to ground level = 1/2 * 59 ft = 29.5 ft

-16t^2 + h0 = 29.5
-16t^2 + 59 = 29.5
-16t^2 = 29.5 - 59
-16t^2 = -29.5

Dividing both sides by -16:
t^2 = (-29.5) / (-16)
t^2 = 1.84375

Taking the square root of both sides:
t = √1.84375
t ≈ 1.36 seconds

Therefore, it will take approximately 1.36 seconds to fall half the distance to ground level.

(b) How long will it take to fall to ground level?
To find this, we need to find the time when the height is equal to 0 (ground level).

-16t^2 + h0 = 0
-16t^2 + 59 = 0

Dividing both sides by -16:
t^2 = 59 / 16
t^2 ≈ 3.6875

Taking the square root of both sides:
t = √3.6875
t ≈ 1.922 seconds

Therefore, it will take approximately 1.922 seconds to fall to ground level.

To find the time it takes for the ball to fall half the distance to ground level, we need to set up an equation and solve for t.

(a) Half the distance to ground level is 59 ft / 2 = 29.5 ft.
The equation for the height of the ball after t seconds is h = -16t^2 + h0, where h0 is the initial height of the ball.

Substituting the given values, we have:
29.5 = -16t^2 + 59

Rearranging the equation, we get:
16t^2 = 59 - 29.5
16t^2 = 29.5
t^2 = 29.5 / 16
t^2 ≈ 1.844

Taking the square root of both sides, we find:
t ≈ √1.844
t ≈ 1.358 seconds

Therefore, it will take approximately 1.358 seconds for the ball to fall half the distance to ground level.

(b) To find the time it takes for the ball to fall to ground level, we need to set up another equation and solve for t.

Setting h equal to zero (ground level), we have:
0 = -16t^2 + 59

Rearranging the equation, we get:
16t^2 = 59
t^2 = 59 / 16
t^2 ≈ 3.688

Taking the square root of both sides, we find:
t ≈ √3.688
t ≈ 1.921 seconds

Therefore, it will take approximately 1.921 seconds for the ball to fall to ground level.

To solve the problem, we need to find the time it takes for the ball to reach certain heights. We'll start by finding the time it takes for the ball to fall half the distance to the ground.

(a) To find the time it takes to fall half the distance to the ground, we need to determine the height when the ball is halfway between the starting height and the ground level.

Given:
Initial height (h0) = 59 ft
Final height (h) = 0 ft (ground level)

By substituting these values into the height equation, we get:
0 = -16t^2 + 59

To solve for 't', we'll set the quadratic equation equal to zero. Rearranging the equation, we have:
16t^2 = 59

Now, we'll divide both sides of the equation by 16:
t^2 = 3.6875

To find 't', we'll take the square root of both sides:
t = √3.6875

Calculating the square root gives us:
t ≈ 1.922 seconds

Therefore, it will take approximately 1.922 seconds for the ball to fall half the distance to ground level.

(b) To find the time it takes to fall to the ground level, we need to determine the time when the height is zero (h = 0 ft).

Using the height equation, we plug in the values:
0 = -16t^2 + 59

Rearranging the equation, we have:
16t^2 = 59

Then, divide both sides by 16 to isolate 't^2':
t^2 = 3.6875

Taking the square root of both sides, we get:
t = √3.6875

Calculating the square root gives us:
t ≈ 1.922 seconds

Therefore, it will take approximately 1.922 seconds for the ball to fall to ground level.

To summarize:
(a) It will take approximately 1.922 seconds for the ball to fall half the distance to the ground.
(b) It will also take approximately 1.922 seconds for the ball to fall to the ground.