# Max height expressed with v, theta, and g

• uber_dzl
That's a good catch, but it's not what the OP is asking for. They want the max height, which would just be h = m * g * (v * sin(theta))^2 / (2 * m * g) or simply (v * sin(theta))^2 / (2 * g).In summary, the max height of a projectile with velocity v at an angle theta using the conservation of energy is (v * sin(theta))^2 / (2 * g).
uber_dzl
[SOLVED] max height expressed with v, theta, and g

## Homework Statement

what is the max height of a projectile with velocity v at an angle theta using the conservation of energy? express in terms of v, theta, and g

1/2*m*v^2=mgh

## The Attempt at a Solution

i tried and got (v^2*sin(theta))/2g (wrong)

You've got the right idea. In fact I think you're close. Actually type out your work and show us, see if you spot the mistake

((1/2)m(v^2)*sin(theta))=mgh...then ((1/2)m(v^2)*sin(theta))/mg=mgh/mg...then the m cancels leaving me with (v^2*sin(theta))/2g=h

is my issue the placement of sin(theta) in the equation before i solve for h?

wow! what a tedious mistake...it was the placement of the exponent and parenthesis that was wrong...

thanx

Well my issue was you start here

1/2*m*v^2=mgh

It's the VERTICAL velocity you care about, it's 1/2*m*Vy^2=mgh

Vy=Vsin(theta) so you get 1/2*m*V^2sin^2(theta)

## 1. What is the formula for calculating maximum height using velocity, angle, and gravity?

The formula for calculating maximum height is:
h = (v2sin2θ) / (2g)
where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## 2. How does changing the launch angle affect the maximum height?

Changing the launch angle will affect the maximum height by changing the vertical component of the initial velocity. The maximum height will be greatest when the launch angle is 90 degrees (vertical launch) and decrease as the angle decreases. The maximum height will be zero when the launch angle is 0 degrees (horizontal launch).

## 3. Is the maximum height affected by the mass of the object?

No, the maximum height is not affected by the mass of the object. The formula for maximum height does not include mass, only initial velocity, launch angle, and acceleration due to gravity.

## 4. Can the maximum height be greater than the initial height?

Yes, the maximum height can be greater than the initial height if the launch angle is greater than 0 degrees. This means that the object is launched at an angle and will reach a higher height than if it was launched straight up.

## 5. How is maximum height related to the range of the object?

Maximum height and range are both affected by the launch angle. The maximum height will occur at the halfway point of the range. This means that the maximum height will be equal to half of the range when launched at an angle of 45 degrees.

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