If a ball is thrown in the air with an initial height of 3
feet, and if the ball remains in the air for 4 seconds,
then accurate to the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is .
[? ] feet

Ask by Jimenez Greene. in the United States

Mar 12,2025

Question

If a ball is thrown in the air with an initial height of 3
feet, and if the ball remains in the air for 4 seconds,
then accurate to the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is .
[? ] feet

Ask by Jimenez Greene. in the United States

Mar 12,2025

UpStudy AI · Accepted Answer

To solve this problem, we can use the kinematic equation for the height of an object in free fall, which is given by:

$$
h(t) = h_0 + v_0 t + \frac{1}{2} a t^2
$$

where:
- $$ h(t) $$ is the height at time $$ t $$,
- $$ h_0 $$ is the initial height,
- $$ v_0 $$ is the initial velocity,
- $$ a $$ is the acceleration (which is negative due to gravity),
- $$ t $$ is the time in seconds.

### Step 1: Identify the known values
- Initial height, $$ h_0 = 3 $$ feet
- Acceleration due to gravity, $$ a = -32 $$ ft/s²
- Time of flight, $$ t = 4 $$ seconds

### Step 2: Determine the initial velocity
Since we are not given the initial velocity $$ v_0 $$, we need to find it. The ball reaches its maximum height at the midpoint of its flight time. Since the total time in the air is 4 seconds, the time to reach maximum height is:

$$
t_{max} = \frac{4}{2} = 2 \text{ seconds}
$$

At maximum height, the velocity will be 0. We can use the following equation to find the initial velocity:

$$
v = v_0 + at
$$

Setting $$ v = 0 $$ at $$ t = 2 $$:

$$
0 = v_0 - 32 \cdot 2
$$

Solving for $$ v_0 $$:

$$
v_0 = 32 \cdot 2 = 64 \text{ ft/s}
$$

### Step 3: Calculate the maximum height
Now we can substitute $$ v_0 $$ back into the height equation to find the maximum height at $$ t = 2 $$:

$$
h(2) = 3 + 64 \cdot 2 + \frac{1}{2} \cdot (-32) \cdot (2^2)
$$

Calculating each term:

1. $$ 64 \cdot 2 = 128 $$
2. $$ \frac{1}{2} \cdot (-32) \cdot 4 = -64 $$

Now substituting these values into the height equation:

$$
h(2) = 3 + 128 - 64
$$

Calculating:

$$
h(2) = 3 + 64 = 67 \text{ feet}
$$

### Final Answer
The maximum height the ball reached is approximately $$ 67 $$ feet.
The ball reached a maximum height of 67 feet.

If a ball is thrown in the air with an initial height of 3
feet, and if the ball remains in the air for 4 seconds,
then accurate to the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is .
[? ] feet

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If a ball is thrown in the air with an initial height of 3 feet, and if the ball remains in the air for 4 seconds, then accurate to the nearest foot, how high did it go? Remember, the acceleration due to gravity on Earth is . [? ] feet

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Physics Questions

If a ball is thrown in the air with an initial height of 3
feet, and if the ball remains in the air for 4 seconds,
then accurate to the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is .
[? ] feet