Question

A ball is launched with initial speed v from the ground level up a frictionless hill. the hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. using conservation of energy, find the maximum vertical height hmax to which the ball will climb. express your answer in terms of v and g.

Answer 1

The ball will rise to a maximum height of $\boxed{h=\dfrac{v^2}{2g}}$.

Explanation:

The kinetic energy of a body is the energy associated with the body by virtue of its motion whereas the potential energy of the body is the amount of energy stored in a body by virtue of its position.

The amount of kinetic energy stored in a body is given by:

$\boxed{K=\dfrac{1}{2}mv^2}$                                                ...... (1)

Here, $K$ is the kinetic energy, $m$ is the mass and $v$ is the speed of the body.

The potential energy stored in a body as it reaches its maximum height is given as:

$\boxed{P=mgh}$                                                      ...... (2)

Here, $P$ is the potential energy stored, $g$ is the acceleration due to gravity and $h$ is the height attained by the body.

According to the conservation of energy, the energy can neither be created nor destroyed. It can only be converted from one form to another.

$\text{kinetic energy}=\text{potential energy}$

Substitute the values of kinetic energy and potential energy and simplify the expression for the maximum height.

$\begin{aligned}\dfrac{1}{2}mv^{2}=&mgh_{max}\\h_{max}=&\dfrac{v^2}{2g}\end{aligned}$

Therefore, the maximum height attained by the ball as it rises up is $\boxed{h_{max}=\dfrac{v^2}{2g}}$.

Learn More:

1. The speed of the quarterback after he throws the ball brainly.com/question/1933971

2. Average power created by the force acting on the sled to move it brainly.com/question/465528

3. The work done on the gas to expand at a constant pressure brainly.com/question/2351427

Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Conservation of Energy

Keywords:

Ball is launched, ground level, conservation of energy, kinetic, potential energy, motion, maximum height, in contact with hill, vertical height, in terms of v and g.

Answer 2

if we take ball then the Kinetic Energy of the ball is ½mV² as it rolls up the slope, the Kinetic Energy is converted to potential energy, PE = mgh. mgh = ½mV² h = V²/2g