# Projectile Motion - motion on a horizontal surface

• bonbloc
In summary, the problem involves finding the maximum height of a projectile that was shot across a horizontal field for 7.6 seconds and traveled 76 meters. By considering the symmetry of the trajectory, it can be determined that the maximum height is reached at the midpoint of the motion, where the vertical velocity is zero. Using this information, the equation of motion can be written and solved to find the maximum height.
bonbloc

## Homework Statement

Isaac Newton shot a dirty snowball 76m across a horizontal field. It passed directly over Edmund Haley's head, and was in the air for 7.6s. How high did it get above the field? Answer in m.

## Homework Equations

Δd = V1(Δt) + 1/2(g)(Δt)^2
and i think some projectile motion equations, not sure if those will help.

## The Attempt at a Solution

since at maximum height the velocity will be zero i tried this:
Δd = 0m/s(Δt) - 1/2(9.8m/s^2)(7.6s)^2
Δd = 283m
but this is not the right answer, so i would appreciate it if someone could help me with this.
Thank you.

Hi bonbloc
At maximum height, velocity (its vertical component, that is) is 0
By symmetry, you can easily see that the maximum height is also reached right in the middle of the trajectory.
So you will have v=0 at T/2 (7.6/2)
From this, you should be able to calculate the vertical component of the velocity.
Write then the equation of motion y(t) which will require this initial value and plug in the found velocity and T/2

Cheers...

Think of the snowball at its high point. It took 7.6/2 = 3.8s to get there (symmetrical trajectory). Now it's stationary & beginning to fall. How far does it fall in the remaining 3.8 sec?

It doesn't matter how far it went horizontally, or what its horizontal velocity was.

## What is projectile motion?

Projectile motion is the motion of an object through the air or another medium under the influence of gravity. It is a form of motion in which an object follows a curved path as it is thrown or launched into the air.

## What is the difference between horizontal and vertical projectile motion?

In horizontal projectile motion, the object only moves in the horizontal direction while in vertical projectile motion, the object moves both horizontally and vertically. This is because gravity only affects the vertical motion of an object, not the horizontal motion.

## What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and the force of gravity. These factors can impact the trajectory, distance, and time of flight of the projectile.

## How do you calculate the range of a projectile?

The range of a projectile can be calculated using the formula R = (V^2sin2θ)/g, where R is the range, V is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This formula assumes no air resistance and a level surface.

## What are some real-life examples of projectile motion?

Some real-life examples of projectile motion include throwing a ball, a javelin throw, a rocket launch, and a bullet fired from a gun. These all involve an object being launched into the air and following a curved path due to the force of gravity.

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