# Solve Speed Problem: Plate Reaches 40m Height & 70m Length

• Kahsi
In summary, the conversation involves a man throwing a plate and calculating its speed using equations for velocity and distance. The initial velocity is 28m/s and the final velocity is -28m/s, resulting in a change of 56m/s. The value for t is calculated incorrectly and the difference between h and s is that h is measured downwards while s is measured upwards.
Kahsi
Hi.

A man is throwing a plate in the air. The plate reaches the height of 40m and the length of 70m. What was the speed of the plate?

This is what I've done

$$v_y:$$

$$mgh = \frac{mv^2}{2} => v = \sqrt{2gh} = \sqrt{2*9,82*40} = 28m/s$$

$$v_x:$$

$$v = v_0 + at => t = 28/9,82 = 2,85s$$

$$s = vt => v = s/t = 70/2,85 = 24,56m/s$$

Code:
                       /|
/  |
/    | v_y = 28m/s
v_z   /      |
/        |
/          |
/            |
/______________|
v_x = 24,6m/s

$$v_z = \sqrt{v_y^2+v_x^2} = \sqrt{24,6^2 + 28^2} = 37m/s$$

But the answer should be 31m/s. What am I doing wrong?

Thank you.

Initial v_y is 28 m/s, but final is -28m/s, so total change is 56m/s and you've calculated t incorrectly; it is actually twice the value you gave.

Thank you for the reply krab.

I have now another question.

We know that
$$mgh = \frac{mv^2}{2} => h = \frac{v^2}{2g}$$
And we also know that $$s = v_0t + \frac{at^2}{2}$$
When it's a free fall $$v_0 = 0$$. That gives us
$$s = -\frac{gt^2}{2}$$

So what's the difference between s and h?

Thank you.

Last edited:
Your expression for h is in terms of the speed v when the object hits the ground.

The object's speed at time t is

v = gt

so t=v/g

Putting this into your expression for s, we get:

$$s = -\frac{gt^2}{2} = -\frac{g}{2}\frac{v^2}{g^2} = -\frac{v^2}{2g} = -h$$

So, as you can see, h and s are the same, apart from the negative sign. The negative sign comes from the fact that in one case you've measured positive distances downwards, and in the other positive distances are upwards.

## What is the formula for calculating speed?

The formula for calculating speed is speed = distance / time.

## How do you calculate the time it takes for the plate to reach a height of 40 meters and a length of 70 meters?

To calculate the time, you need to know the speed of the plate. Then, you can use the formula time = distance / speed. In this case, the distance is 70 meters and the speed can be calculated by dividing the distance by the time it took to reach 40 meters.

## What are the units of measurement for speed?

The units of measurement for speed can vary, but some common units include meters per second, kilometers per hour, and miles per hour.

## Can you determine the speed of the plate if you only know the distance and time it took to reach a height of 40 meters and a length of 70 meters?

Yes, you can use the formula speed = distance / time to calculate the speed of the plate. However, it is important to note that this will only give you the average speed over the entire distance. To get a more accurate measurement, you would need to calculate the speed at different points along the distance.

## How can you use the speed of the plate to predict its future motion?

The speed of the plate can be used to predict its future motion by calculating the distance it will travel in a given amount of time. This can be done using the formula distance = speed * time. Additionally, the speed can also be used to determine the force and energy required for the plate to reach certain heights and lengths.

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