# Question about speed of a projectile

• vande060
In summary, the problem is to find the speed of a horizontally launched projectile with initial speed v0 and height h above the origin, as a function of x. The equations for x and y are x = v0t and y = h - 1/2*g*t^2. Using these equations and differentiating, the velocity can be found as y(x)' = (-g*x)/v0^2 and x' = v0. Substituting these into the formula for speed, s = (v^2x + v^2y)^1/2, the speed can be expressed as a function of x.
vande060
1. Homework Statement

If a projectile is launched horizontally (in direction of increasing x) with initial speed v0, from a height h above the origin, find its speed s = (v^2x + v^2y)^1/2 as a function of x

2. Homework Equations

so far i have the equations for x and y

y= h - 1/2*g*t^2

x= v0*t

3. The Attempt at a Solution

i don't understand how to do this problem in the least

bump

i was thinking,

x = v0t

t = x/v0

y = h - 1/2*g*t^2

substituting for t

y(x) = h - 1/2*g*(x^2/v0^2)

differentiating to get the velocity

y(x)' = (-g*x)/v0^2

and

x' = v0

then i can put this in the formula

s = (v^2x + v^2y)^1/2

s = (v0^2 + [(-g*x)/v0^2]^2)^1/2

to get speed as a function of x. i don't know if this is right, but its a shot

Last edited:

## 1. What is the definition of speed?

Speed is the rate at which an object moves in a given direction. It is a scalar quantity, meaning it only has a magnitude and no specific direction.

## 2. How is speed calculated?

Speed is calculated by dividing the distance traveled by the time it took to cover that distance. It is represented by the formula: speed = distance / time.

## 3. What is the difference between speed and velocity?

While speed is a scalar quantity, velocity is a vector quantity. Velocity takes into account both the speed and direction of an object's motion. So, an object can have the same speed but different velocities if it is moving in different directions.

## 4. How does the speed of a projectile change over time?

The speed of a projectile changes over time due to the force of gravity. As the projectile moves upwards, gravity slows it down until it reaches its peak height. Then, as it falls downwards, gravity accelerates it, increasing its speed until it hits the ground.

## 5. Can the speed of a projectile be constant?

Yes, the speed of a projectile can be constant if there are no external forces acting on it, such as air resistance or gravity. In this case, the projectile would continue to move at a constant speed in a straight line until acted upon by an external force.

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