# Kinematics problem, ball drop.

• AlchemistK
In summary, a ball rolls off a staircase with three steps that are 10 cm high and 20 cm wide. The question asks for the minimum horizontal velocity needed for the ball to hit the lowest step directly. The equation used to solve this problem is s=u*t+1/2 a*t^2. However, the attempt at a solution was incorrect as it calculated the average speed instead of the initial horizontal speed needed for the ball to hit the lowest step. The correct approach involves finding the initial horizontal velocity using two equations, (1/2)at^2=0.2 and uxt=0.4.
AlchemistK

## Homework Statement

A staircase contains three steps each of 10 cm high and 20cm wide(refer attachment).What should be the minimum horizontal velocity if a ball rolling off the uppermost plane so as to hit directly the lowest plane?

## Homework Equations

s= u*t + 1/2 a*t^2

## The Attempt at a Solution

In the vertical motion,
s= u*t + 1/2 a*t^2
=> 0.3 = 0 + 1/2 * 10 * t^2
=>t= $\sqrt{}6$ /10 s

therefore, v=s/t => 2.45 m/s

Where did i go wrong? The given answer is 2 m/s and i don't believe that its an approximation.

#### Attachments

• untitled.bmp
47.1 KB · Views: 514
I don't really see what you are doing. You start off by assuming that u, the initial vertical speed, is 0, which is true, and caluculate the time it will take to go down 0.3 meters. Finally, you calculate the average speed over that time. That was not what was asked. You are asked for the initial horizontal speed, ux, required so that the ball hits the lowest step. That is, you must find u such that the ball misses the second step. When the vertical drop is 0.2 meters, the horizontal motion must be at least 0.4 m. You have two equation: (1/2)at^2= 0.2, ux t= 0.4. Solve for ux.

Atul Saswat
You did the last step wrong. You can't perform v=s/t because acceleration is there in the situation. But that's not for initial velocity asked in the question. Follow HallsofIvy advise.

Ahhh yes, i get it now, thank you.

## 1. What is a kinematics problem?

A kinematics problem is a type of physics problem that involves analyzing the motion of objects without considering the forces that cause the motion. It focuses on concepts such as displacement, velocity, and acceleration.

## 2. How do you solve a kinematics problem?

To solve a kinematics problem, you need to first identify the variables given in the problem, such as initial velocity, acceleration, and time. Then, you can use equations such as the equations of motion or the kinematic equations to solve for the unknown variables.

## 3. What is a ball drop kinematics problem?

A ball drop kinematics problem involves analyzing the motion of a ball as it falls from a certain height under the influence of gravity. This type of problem typically requires you to find the ball's final velocity, displacement, or time of flight.

## 4. How is gravity involved in a ball drop kinematics problem?

Gravity is the force responsible for the ball's downward motion in a ball drop kinematics problem. It causes the ball to accelerate towards the ground at a constant rate of 9.8 m/s², which is the acceleration due to gravity on Earth.

## 5. What are some common mistakes to avoid when solving a ball drop kinematics problem?

Some common mistakes to avoid when solving a ball drop kinematics problem include using the wrong units, not properly labeling the variables, and not checking the reasonableness of your answer. It is also important to remember to use the correct equations and to carefully follow the steps in the problem-solving process.

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