Projectile motion was first seriously studied scientifically by Galileo. Who used a custom designed apparatus to study the motion of projectiles. Projectiles are object in motion that occurs in two dimensions - horizontally and vertically.
What Galileo discovered were two important principles in projectile motion.
Firstly, the horizontal component of the velocity can be described as a constant velocity. Vertically however, the motion was at a constant acceleration, resulting in an increase in displacement that is proportional to the square of the time travelled
Secondly, and crucially, these two motions are independent of each other - what occurs vertically does not affect what happens horizontally.
In essence its two separate motions as right angles to each other, one with a constant acceleration, the other at constant velocity.
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Theory
Let us explore this more closely, including the mathematical analysis required to understand projectile motion This video explores the concept with a number of sample situations. |
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Check your understanding
Sample Problems
We are now ready to try some sample problems
Below are sample problems with videos that explain how to solve them. It is suggested you try the problems beforehand, as this actually aids understanding, even if you are unsure if you are correct.
We are now ready to try some sample problems
Below are sample problems with videos that explain how to solve them. It is suggested you try the problems beforehand, as this actually aids understanding, even if you are unsure if you are correct.
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Lets Play
Let's now test your understanding. The following pHET animation explores projectile motion.
First, become familiar with the interactive.
Let's now test your understanding. The following pHET animation explores projectile motion.
First, become familiar with the interactive.
- Start with the intro option.
- Fire a few rounds off, adjusting the initial parameters of height, velocity and angle.
- Click on the velocity and acceleration vectors, and see how the projectile behaves.
- Next, set the various variables to your choosing, and DETERMINE the range by doing the calculations.
- Then set the target to the predetermined ranges and see if you have the correct result.
More problems to try
- A bullet is fired from a rifle that is held 1.6 m above the ground in a horizontal position. The initial speed of the bullet is 1100 m/s. Find
(a) the time it takes for the bullet to strike the ground and
(b) the horizontal distance traveled by the bullet. (629m) - A major league pitcher can throw a baseball in excess of 41 m/s. If a ball is thrown horizontally at this speed, how much can it be expected to drop due to gravity by the time it reaches a catcher who is 17 m away from the point of release? Pitcher’s mounds are raised to compensate for this drop. (0.84m)
- A horizontal rifle is fired at a bull’s eye. The muzzle speed ofthe bullet is 670 m/s. The barrel is pointed directly at the center of the bull’s eye, but the bullet strikes the target 2.5 cm below the center. What is the horizontal distance between the end of the rifle and the bull’s eye?( 47.9 m)
- A jet fighter is traveling horizontally with a speed of 111 m/s at an altitude of 300 m, when the pilot accidentally releases an outboard fuel tank.
(a) How much time elapses before the tank hits the ground. (7.82s)
(b) What is the velocity of the tank (magnitude and direction) just before it hits the ground? (134.9 m/s)
I have got these from a variety of sources, some my own, some from elsewhere. Lots of practice here
- projectile practice
- projectiles 1 answers included
- projectiles 2
- projectiles 3
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