# How would i derive the equation?

• Tensaiga
In summary, the two balls will pass at the same height above the ground when the initial velocities are the same and the acceleration is three times the magnitude of the deceleration.
Tensaiga
Question 1:
A ball is dropped from the top of a building and it strikes the ground with a speed of v m/s. From ground level, a second ball is thrown straight upward with the same initial speed of v m/s at the same instant that the first ball is dropped. Ignoring air resistance, determine at what height above the ground the two balls will pass.

Question 2:
A cab driver picks up a customer and delivers her 2.0km away after driving along a striaght route. In making the trip, the driver accelerates uniformly to the speed limit and upon reaching it, decelerates uniformly immediately. The magnitude of the deceleration is three times the magnitude of the acceleration. Calculate the distance traveled during the acceleration and deceleration phases of the trip.

Question 3:
A vehicle spped trap is set up with pressure activiated strips across the highway, 110 meters apart. a car is diring along at 33m/s in a area where the speed limit is 21m/s. At the instant the vehicle activates the first strip, the driver begins slowing down uniformly. What is the minimum deceleration need in order that the average speed of the vehicle between the strips does not exceed the speed limit.

I have no idea on how to start on these problems... so i have tried it, but i can't get a clear idea to begin with.

Thanks.

Last edited:
For #1 you can express the height of the building in terms of the final velocity v. You can then write two equations for the vertical positions of the balls in terms of their initial positions relative to the ground, initial velocities, acceleration, and time. Find the time and the vertical height when they have the same vertical height.

umm well i got two equations, the first one would be D=1/2at^2, (downward ball after it has reached the highest point then free fall.), the second would be D=v/mst-1/2at^2, upward motion slows down by gravity. then?

Tensaiga said:
umm well i got two equations, the first one would be D=1/2at^2, (downward ball after it has reached the highest point then free fall.), the second would be D=v/mst-1/2at^2, upward motion slows down by gravity. then?
Express both of your equations in the same form and with the same reference point. Use the general equation

y = y_o + v_o*t - ½*g*t²

For the ball that is dropped, you need to find y_o. You can do that knowing that when it hits the ground (y = 0) its velocity is -v, and it started from rest, so the change in velocity is -v - 0 and that change is due to the acceleration acting for some time -gt. An equatioin has already been worked out based on this reasoning that involves the velocities, acceleration, and distance moved. You can use that equation if you prefer. Once youu get the two equation in the form written above. All you have to do is find the t and y value that makes the y and t in both equations the same.

## Question 1: What is the process of deriving an equation?

The process of deriving an equation involves using mathematical principles and rules to manipulate and rearrange existing equations to solve for a specific variable or relationship between variables.

## Question 2: How do I know which equations to use when deriving an equation?

The equations used in deriving an equation will depend on the specific problem or scenario being investigated. It is important to carefully analyze the problem and identify the known variables and relationships between them in order to determine which equations are relevant.

## Question 3: Can I derive an equation without any prior knowledge of math?

No, deriving an equation requires a basic understanding of mathematical principles and equations. It is not possible to derive an equation without any prior knowledge of math.

## Question 4: What are the most common methods used in deriving equations?

The most common methods used in deriving equations include substitution, elimination, and rearranging equations. These methods involve manipulating existing equations to solve for a specific variable or relationship between variables.

## Question 5: Is there a specific order in which I should solve equations when deriving an equation?

There is no specific order in which equations must be solved when deriving an equation. However, it is important to keep track of any substitutions or rearrangements made in order to avoid errors and ensure the final derived equation is accurate.

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