a girl throws a stone vertically upward with an initial speed of 8 m/s. How high will the stone rise? How long will it take to return to the ground after it is thrown?

Question

a girl throws a stone vertically upward with an initial speed of 8 m/s. How high will the stone rise? How long will it take to return to the ground after it is thrown?

Answer 1

that isnt much to go on, but try this:

h(t)=-1/2(g)(t^2)+Vt+h
(g=32ft/sec^2 or 9.8m/sec^2)
V=initial velocity
t=time
h=initial height
im assuming that this question is implying that the girl is standing on the ground, so for "h" no input would be needed.
that function up there is quadratic btw, so you could estimate the roots to find your answer. And possibly use a quadratic calculator, id give you a link if it would let me, but you could just google it...probably not too terribly helpful lol but I was kinda looking for a second opinion myself so...sorry :/

Answer 2

To determine how high the stone will rise and how long it will take to return to the ground, we can use basic kinematic equations. Let's break down the problem step by step:

1. First, we need to calculate the maximum height reached by the stone. We can use the equation for vertical displacement in free fall:

𝑑 = 𝑣₀²/ (2𝑔)

where 𝑑 is the displacement, 𝑣₀ is the initial velocity, and 𝑔 is the acceleration due to gravity (which is approximately 9.8 m/s² on Earth).

Plugging in the given values, we have:

𝑑 = (8 m/s)² / (2 × 9.8 m/s²)

2. Using this equation, we can calculate the displacement 𝑑, which represents the maximum height reached by the stone.

3. Next, let's find the time it takes for the stone to reach its maximum height. We can use the equation for time:

𝑡 = 𝑣₀ / 𝑔

Plugging in the given values:

𝑡 = 8 m/s / 9.8 m/s²

4. This time represents the time it takes for the stone to reach its maximum height. However, since the stone will eventually return to the ground, we need to double this time to calculate the total time it takes for the stone to return to the ground.

Now, let's calculate the values:

1. 𝑑 = (8 m/s)² / (2×9.8 m/s²)

2. Solve for 𝑑 to get the maximum height.

3. 𝑡 = 8 m/s / 9.8 m/s²

4. Multiply 𝑡 by 2 to obtain the total time for the stone to return to the ground.

By following these steps and performing the calculations, you will find the answers to both questions.