suppose you and your friend are standing at the edge of a cliff your friend drops a stone straight down and with great speed you throw a similar stone horizontally the question is which stone will land on the water surface last does your intuition tell you that since you threw the stone with greater speed the stone will take more time to land if so you are wrong both stones will actually land at the same time welcome to the interesting world of projectile motion let's go over some fundamental concepts when you throw a ball at an angle it never goes straight like this instead it will have an elegant curved path more specifically a parabolic path this kind of projectile motion happens due to the effect of gravity when thrown at an angle the object has two components of velocity one horizontal and one vertical the gravitational force always acts vertically when a force acts on a moving object vertically the horizontal component of velocity never changes only the vertical component of the object's velocity will change due to the vertical force therefore the initial horizontal component of velocity you have given will also not change throughout the motion of the object let's analyze this more closely and see how the variation of the vertical component of velocity affects the shape of the trajectory the horizontal and vertical distance traveled by the object for a small time interval is shown here its complete motion will be as shown since the horizontal component of velocity does not change with time with an equal time interval the ball will travel the same distance horizontally however the vertical component of velocity has been reduced due to the effect of gravity thus the distance traveled vertically in this time interval will be lesser just continue this logic for a few more intervals you can clearly see the object is taking a curved path as the vertical velocity keeps on decreasing as the ball travels up the point where the vertical velocity becomes zero will be the maximum height it can achieve after this point the vertical velocity will become negative and the object will start its descent during the descent the gravitational force and velocity are in the same direction so the vertical velocity will keep increasing this will be the final shape traced by the ball the shape of this trajectory is known as a parabola here's an interesting thought experiment this cannon is ejecting a ball perfectly vertically the ball will come back to its initial position or zero movement in the horizontal direction now let's reduce the angle and eject it with the same speed now the ball can travel horizontally with a little more angle reduction the range increases further when the cannon's angle is down to 45 degrees the range becomes even higher however if you increase the angle after 45 degrees the outcome is different the range actually decreases the maximum range is at an angle of 45 degrees before and after that the range decreases can you guess the reason behind this the range of the ball is multiplication of the initial horizontal velocity you have given multiplied by the time duration it stays in the air the time the ball spends in the air decreases as you decrease the angle however the horizontal velocity keeps on increasing as you reduce the angle multiplication of two numbers will be maximum when both the factors have a good value in this case the time the ball spent in the air and horizontal velocity has a good value at the angle of 45 degrees this is why you get maximum range when you throw the ball at 45 degrees with this understanding of projectile motion it becomes quite easy to solve the question we posed at the beginning of the video the time it takes for the stone to hit the ground depends only on its vertical velocity even if you have given a high horizontal velocity to your stone its vertical component is zero this means both the stones have the same vertical component of velocity at the beginning zero this velocity will increase over time due to the effect of gravity but with the same magnitude this means the vertical component of velocity of both stones is the same throughout their travel therefore both will hit the ground at the same time pretty interesting right the greater speed you have given to the stone has no effect at all on its travel time because you threw the stone perfectly horizontally thank you for watching we hope you enjoyed the video see you next time