# Projectile Motion Angle Problem

• TRobison
In summary, the problem involves a projectile being shot from a cliff at an angle of 37.0 degrees with an initial speed of 115m/s. The time taken for the projectile to hit the ground, range, horizontal and vertical components of velocity, magnitude of velocity, angle made by the velocity vector with the horizontal, and maximum height above the cliff top reached by the projectile are all calculated using various equations. The quadratic formula is used to solve for the time and only one solution is physically meaningful.
TRobison

## Homework Statement

A projectile is shot from the edge of a cliff (h=265m) above ground level with an initail speed of Vi= 115m/s at an angle of 37.0 degrees with the horizontal.

a. Determine the time taken by the projectile to hit point P at ground level?
b. Determine the Range of the projectile as meaured from the base of the cliff
c. At the instant just before the projectile hits point P, find the horizontal and the vertical components of its velocity.
d. What is the magnitude of the velocity?
e. What is the angle made by the velocity vector with the horizontal?
f. Find the maximum height above the cliff top reached by the projectile.

## Homework Equations

a. y=y 0 +v 0 t+(1/2)at 2
b. R=(V o^2 Sin 2∅)/g
c. ?
d. ?
e. ?
f. ?

## The Attempt at a Solution

Sorry if this seems to easy for you, but I'm 48 and my math skills aren't as sharp as they used to be. I am particualary stuck on trying to solve for the time. How do Solve for t? forgot the rules on how to factor out the t, so here is what I had:

y=265m=(69.2087)(t)-(1/2)(9.8)(t)^2

Welcome to PF TRobison:

When the projectile hits the ground, the vertical position is y = 0. So the equation becomes:

0 = y0 + v0t - (1/2)gt2

where y0 is the initial vertical position, which = h = 265 m

v0 is the initial vertical speed, which you have to solve for using the total speed and launch angle, using trig (it looks like you already did this correctly, to get 69.2 m/s).

This equation is a quadratic equation for t. It's not obviously factorable, so to solve it, you need to use the quadratic formula:

Any quadratic equation has two roots, which means that you will get two solutions using this formula: there will be TWO values of t for which y = 0, since the y vs. t curve is a parabola. However, only one of them will be physically meaningful. The other one will be negative, since if you extrapolate the parabolic trajectory to times before t = 0, the path will eventually intersect the ground again. Of course, this didn't actually happen, and times before t = 0 are not meaningful here.

Thanks for putting me the right direction, I'm now calculating a total time of 17.05s my range seems too large, 1565.9m, but will continue with the rest of the problem to see how it comes out. Again thanks for your help.

## What is projectile motion angle problem?

The projectile motion angle problem is a physics concept that involves calculating the motion of an object that is launched into the air at an angle. It takes into account the initial velocity, angle of launch, and gravitational force to determine the trajectory and landing point of the object.

## How do you calculate the angle for maximum range in projectile motion?

The angle for maximum range in projectile motion can be calculated using the formula tan θ = (v0²/g), where θ is the angle of launch, v0 is the initial velocity, and g is the acceleration due to gravity. This formula can be rearranged to solve for θ, which will give the angle at which the object will travel the farthest distance.

## What is the relationship between angle and range in projectile motion?

The relationship between angle and range in projectile motion is that the angle of launch directly affects the range, or horizontal distance traveled, of the object. The higher the angle, the shorter the range, and the lower the angle, the longer the range. The angle for maximum range is typically around 45 degrees.

## What happens to the range when the angle of launch is increased or decreased?

When the angle of launch is increased, the range of the projectile decreases. This is because the vertical component of the initial velocity increases, causing the object to reach its peak height sooner and then fall to the ground at a shorter horizontal distance. Conversely, when the angle of launch is decreased, the range of the projectile increases.

## What are the applications of projectile motion angle problem in real life?

The projectile motion angle problem has many applications in real life, including sports such as basketball, football, and baseball, where players must calculate the angle and velocity needed to make a successful shot or pass. It is also used in engineering and construction to determine the trajectory of projectiles and the safety of structures. Additionally, it is used in military and defense technology to calculate the trajectory of missiles and other weapons.

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