SOLUTION: The range of a projectile is the horizontal distance it travels before it reaches the ground. The greatest range is achieved if the projectile is thrown at 45° to the horizontal.

Question 1200490: The range of a projectile is the horizontal distance it travels before it reaches the ground. The greatest range is achieved if the projectile is thrown at 45° to the horizontal.
A ball is thrown with an initial velocity of 40 ms^-1, Calculate its greatest possible range when air resistance is considered to be negligible.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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The range of a projectile is the horizontal distance it travels before it reaches the ground.
The greatest range is achieved if the projectile is thrown at 45° to the horizontal.
A ball is thrown with an initial velocity of 40 ms^-1, Calculate its greatest possible range
when air resistance is considered to be negligible.
~~~~~~~~~~~~~~~~~

So, the angle to the horizon of the initial velocity is assumed to be 45°.


At this condition, the horizontal component of the velocity is 

     = 40*cos(45°) = 40*(sqrt(2)/2) = 40*0.707 = 28.285 m/s;


The vertical component of the velocity is

     = 40*sin(45°) = 40*(sqrt(2)/2) = 40*0.707 = 28.285 m/s  

(has the same numerical value as the horizontal component).


The flight time is  t =  =  = 5.767 seconds (approximately).


    Here g = 9.81 m/s^2  is the gravity acceleration at the Earth surface.


The horizontal distance to fly (the range) is   = 28.285*5.767 = 163.120 m (rounded).


ANSWER.  The greatest possible range is approximately 163.120 m under given conditions.

Solved.

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