Find Distance of Projectile Fired with an Initial Velocity - Help Needed

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In summary, to find the distance from launching to landing points when a projectile is fired over level ground with an initial velocity of 20 m/s in the vertical direction and 30 m/s in the horizontal direction, you can use the formula √30² + 20² to find the magnitude of the resultant vector. Then, find the flight time by calculating how long it takes for gravity to reduce the initial vertical velocity to zero, which is equal to the "time to go up" and "time to go down". Finally, multiply the horizontal velocity by the flight time to get the distance, which in this case is 120m.
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roam
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A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s. Using g = 10 m/s², find the distance from launching to landing points.



I don't know what formula to use to solve this question. I would appreciate your help.



I start off by finding the magnitude of the resultant vector: √30² + 20², then I don't know what to do next...
 
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Relate the time, velocity, and distance in the x-direction with the time, distance, velocity, and acceleration in the y direction.
 
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So this how you do it:
Horizontal velocity multiplied by flight time equals range.

Find the flight time by working out how long it will take for gravity to reduce the initial vertical velocity to zero. This gives you the "time to go up" and this will be equal to the "time to go down".

a=Δv/Δt so if g=-10ms-2 then:
Δt=Δv/g=0-20/-10=2s so total flight time is 4s.

Now just multiply the horizontal velocity by the flight time 30*4=120m

:smile:
 

1. What is a projectile and how is it different from a regular object?

A projectile is any object that is thrown, launched or shot through the air, typically with some initial velocity. It is different from a regular object because it follows a curved path due to the influence of gravity.

2. How do you calculate the distance of a projectile fired with an initial velocity?

The distance of a projectile can be calculated using the formula d = v0t + ½at2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (usually taken as -9.8 m/s2).

3. What factors can affect the distance of a projectile fired with an initial velocity?

The distance of a projectile can be affected by several factors, including the initial velocity, angle of launch, air resistance, and the mass of the projectile.

4. How can the initial velocity of a projectile be determined?

The initial velocity of a projectile can be determined by measuring the horizontal and vertical components of the projectile's motion. This can be done using a motion detector or by measuring the displacement and time taken for the projectile to travel a known distance.

5. Can the distance of a projectile be calculated if the initial velocity is not known?

Yes, the distance of a projectile can still be calculated if the initial velocity is not known. In this case, the initial velocity can be eliminated from the formula by using the relationship between the horizontal and vertical components of the projectile's motion.

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