# How do I find the final velocity and how high the bridge is?

• Julia Smith
In summary, a rock is thrown upward from a bridge with an initial velocity of 2.0 m/s and takes 4.0 seconds to hit the water below. The final velocity of the rock as it hits the water is -38 m/s. To find the height of the bridge, we can use the equation s = ut + ½at2, where s is the displacement due to the acceleration of -10m/s^2.
Julia Smith

## Homework Statement

A rock that is thrown upward from a bridge with an initial velocity of 2.0 m/s. (Assume there is no air drag: a = -10m/s2).
a) If the rock takes 4.0 s to hit the water below once the rock is released. What is the final velocity of the rock as it hits the water?
b) How high is the bridge?

## Homework Equations

v = u +at
x = x0 + vit + 1/2*a*t2

## The Attempt at a Solution

For (a), I know that the equation I can use is v = u + at. u being initial velocity.
v = (2.0m/s) + (-10m/s2) (4.0s)
v = -38 m/s

However, for (b), I do not know how I can solve it and need help on that ASAP

Julia Smith said:
for (b), I do not know how I can solve it
Your second relevant equation looks useful.

Hi Julia Smith.

Your equation is right if x is displacement, so just treat xo as zero.

I'd prefer the equation be written using s for displacement, viz.,
s = ut + ½at2

where s is the displacement due to this acceleration.
You can throw in a term so if you wish, but it seems an unnecessary complication.

## 1. How do I find the final velocity of an object?

To find the final velocity, you will need to know the initial velocity, acceleration, and time. You can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

## 2. How do I calculate acceleration?

Acceleration can be calculated using the equation a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time. Alternatively, if you have the distance (d) and time (t), you can use the equation a = 2d/t².

## 3. How can I determine the height of a bridge using the final velocity of a falling object?

You can use the equation d = (vf² - vi²)/(2a), where d is the height of the bridge, vf is the final velocity, vi is the initial velocity (in this case, 0 m/s), and a is the acceleration due to gravity (9.8 m/s²).

## 4. Why is it important to know the final velocity and height of a bridge?

Knowing the final velocity and height of a bridge is important for safety purposes. It can help engineers determine the strength and stability of the bridge, and ensure that it can withstand the impact of falling objects.

## 5. Are there any other factors that may affect the final velocity and height calculation?

Yes, there are other factors that may affect the final velocity and height calculation, such as air resistance and the shape of the falling object. However, these factors can be accounted for in the calculation by using more complex equations or by conducting experiments to gather more accurate data.

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