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College Physics (Urone)
Found in: Page 124

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Short Answer

Derive R=Vo2sin2θogfor the range of a projectile on level ground by finding the time at which becomes zero and substituting this value of into the expression for X1 X0 , noting that R=X1 X0.

The range of the projectile motion is derived as required.

See the step by step solution

Step by Step Solution

Step 1: Definition of initial velocity

When gravity first exerts force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.

Step 2: Stating given data

The velocity can be said to be Vi. The velocity is making some angle with the x axis.


The displacement will be Y=0 meters.

The time is not given.

The gravitational acceleration is -9.8m/s2-9.8m/s2.

Step 3: Deriving parabolic trajectory of displacement

The initial velocity and the final velocity and the average velocity will be same.


Now let’s calculate the displacement.

Y=Viy+12gyt20=Visinθ×t+12(-g)(t)2 12(g)(t)2=Visinθ×t12(g)(t)=Visinθt=2Visinθg

The time when displacement is zero is in the above equation.

The average velocity will be equal to the x component of initial velocity.




Putting the values of v and t into the above equation, we have


Hence the range of the projectile motion is derived as above.

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