# Projectile motion. how long does it take for the projectile to git the ground?

• hello_there
In summary, the problem at hand involves finding the time it takes for a projectile to hit the ground when fired at an initial height of h, elevation angle of a, and speed of v. However, the use of normal physics equations is not allowed and instead, maths must be used. It is impossible to solve the problem without incorporating the acceleration due to gravity, so it is unclear what equations are allowed. It is suggested that a quadratic equation may be used and that there may be an allowed equation that contains the gravitational acceleration g.
hello_there
I have no idea on where to start with this. Also we are not allowed to use The normal physics equations, we have to use maths.

At time t = 0 a projectile is fired from a height of h above level ground at an elevation angle
of a and a speed of v.

Show that the time when the projectile hits the ground will be
t =(vsin(a) + Sqrt( v2sin2(a) + 2hg))/g

thanks

hello_there said:
Also we are not allowed to use The normal physics equations, we have to use maths.

Can you elaborate on this? It's obviously impossible to solve the problem without incorporating the acceleration due to gravity.

we we told we can't use the equations like v=u+at and v^2= u^2 + 2as to work it out

Hmmm, are you allowed to use the fact that the trajectory is a quadratic equation? It's hard to guess what's allowed without knowing what was presented in class. Is there an allowed equation that contains the gravitational acceleration g?

i guess we have to use a quadratic equation or there would be no way to do it, I'm just not sure how to incorperate g into the equation

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It is a type of motion that follows a parabolic path.

## 2. What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity of the object, the angle of launch, the mass of the object, and air resistance.

## 3. How does gravity affect projectile motion?

Gravity is the force that pulls the projectile towards the ground. As the object moves through the air, gravity causes it to accelerate towards the ground at a constant rate of 9.8 meters per second squared.

## 4. How can we calculate the time it takes for a projectile to hit the ground?

The time it takes for a projectile to hit the ground can be calculated using the formula t = 2 * (v * sinθ) / g, where t is the time, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

## 5. Does the mass of the object affect the time it takes for a projectile to hit the ground?

No, the mass of the object does not affect the time it takes for a projectile to hit the ground. The only factors that affect the time are the initial velocity and the angle of launch.

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