Given 2 Sets of Data, Find 3rd (Velocity, Acceleration?)

In summary, it takes 7.5 seconds to reach the ground from 70 yards. The equations used to solve this problem are h=h_{0}-v_{0}t-\frac{1}{2}at^{2}. The initial height and the time for the body to fall to the ground (h=0) are given.
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Homework Statement


Falling 20 yards above the ground takes 6 seconds to reach the ground.

Falling 100 yards above the ground takes 9 seconds to reach the ground.

How long would it take to reach the ground from 70 yards?

Homework Equations


v=d/t ?I'm completely clueless. Any help with this would be greatly appreciated! Thank you.
 
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  • #2
It's best to assume that body is accelerating at [itex]a[/itex] with initial speed [itex]v_{0}[/itex] and height [itex]h_{0}[/itex]. Maybe some assumptions aren't true, but we don't know that before we try to solve the problem.

So, what you actually have is two equations of the form

[tex]h=h_{0}-v_{0}t-\frac{1}{2}at^{2}.[/tex]

You are given the initial height and the time after which body falls on the ground (to the height [itex]h=0[/itex]). That's all information you need.
 

What is the difference between velocity and acceleration?

Velocity is a measure of how fast an object is moving and the direction of its motion. Acceleration, on the other hand, is the rate of change of an object's velocity over time. In other words, velocity tells us how fast an object is moving, while acceleration tells us how much an object's velocity is changing.

How do you calculate velocity?

Velocity is calculated by dividing the change in an object's position (displacement) by the time it took for that change to occur. In mathematical terms, this can be written as v = Δx/Δt, where v is velocity, Δx is displacement, and Δt is time.

What are the units of velocity and acceleration?

The units of velocity are typically meters per second (m/s) or kilometers per hour (km/h). Acceleration, on the other hand, is typically measured in meters per second squared (m/s^2). However, other units such as miles per hour per second (mph/s) or feet per second squared (ft/s^2) may also be used.

How do you find the third set of data when given two sets of data for velocity and acceleration?

To find the third set of data, you can use the equations of motion. These equations relate displacement, velocity, acceleration, and time. By plugging in two of the given values and solving for the third, you can find the missing set of data.

What are some real-life applications of finding the third set of data for velocity and acceleration?

The ability to find the third set of data for velocity and acceleration is crucial in many fields, including physics, engineering, and sports. For example, engineers may use this information to design safer vehicles or structures. In sports, coaches and athletes can use this data to analyze and improve performance. Additionally, understanding velocity and acceleration can also help predict and prevent accidents in fields such as transportation and aviation.

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