# Projectile Motion: Calculating Range, Maximum Height, Speed & Angle

• miley1234
In summary, the conversation discusses projectile motion and provides information on calculating the horizontal range, maximum height, speed, and angle of motion of a projectile. The initial velocity is given as (8.8i+4.5j) m/s and the time of observation is 2.7 seconds. The initial horizontal velocity remains constant while the vertical velocity experiences negative acceleration. To calculate the speed, the vertical and horizontal velocity components are added together, and the angle of projection can be determined by finding the tangent of the two components.

#### miley1234

Urgent! projectile motion

Heyy every1
Q Exactly 2.7s after a projectile is fired into the air from the ground ,it is observed to have a velocity v = (8.8i+4.5 j) m/s where the x-axis is horizontal and the y-axis is positive upward .
a)Determine the horizontal range of the projectile
b)Determine the maximum height above the ground
c)Determine the speed of motion just above the projectile strikes the ground .
d)Determine the angle of the motion just before the projectile strikes the ground .

I managed to do the first two parts where max height is 49m and range is 56 m .Bt i do not noe how to go abt the c) and d) part

What is horizontal component of the velocity? What is the vertical component of final velocity?

well i was able to calaculate the max height and range using horizontal velocity to be 8.8 and vertical final velocity as 4.5 at 2.7 s .This much information only was given n the question tht s why i m confused

For d), knowing the horizontal and vertical components of initial velocity should help you. You know that the trajectory is parabolic and so just prior to impact, use the condition,$$-v_{fy} \hat{y} = v_{oy} \hat{y}.$$

Horizontal velocity(i component) remains constant since no forces acting on it.
Vertically(j component) there is negative acceleration.
Sketch a graph of velocity vs. time. Upward as positive.
Δv/Δt is constant. You can find initial vertical velocity from acceleration equation.

Speed it the vector sum of vertical and horizontal velocity.

Angle of projection is just the tangent of vertical and horizontal velocity.

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## 1. What is urgent projectile motion?

Urgent projectile motion is when an object is launched or thrown with a specific initial velocity and angle, and its motion is affected by gravity and air resistance. This type of motion is urgent because it involves quick and sudden movement.

## 2. What are the key factors that affect urgent projectile motion?

The key factors that affect urgent projectile motion are the initial velocity of the object, the angle at which it is launched, the force of gravity, and the presence of air resistance.

## 3. How is the trajectory of an urgent projectile calculated?

The trajectory of an urgent projectile can be calculated using mathematical equations, taking into account the initial velocity, launch angle, and acceleration due to gravity. These equations can be solved using principles of calculus.

## 4. What is the maximum height reached by an object in urgent projectile motion?

The maximum height reached by an object in urgent projectile motion depends on the initial velocity and the launch angle. The higher the initial velocity and the smaller the launch angle, the higher the maximum height will be.

## 5. How does air resistance affect urgent projectile motion?

Air resistance can significantly affect urgent projectile motion by slowing down the object and changing its trajectory. The presence of air resistance can cause the object to reach a lower maximum height and travel a shorter distance compared to a scenario with no air resistance.