velocity question!?

Question

3 balls with the same mass is shot. Ball 1 is shot vertically up, ball 2 is shot horzontally, and ball 3 is shot vertically down. List the speed of the ball as they hit the ground, inorder from largest to smallest. and Explain.

Is all the velocities the same? because only gravity is affecting the speed? Thankyou

Answer 1

Let's think of this conceptually. When a ball is thrown horizontally, the only change in its velocity (in a vertical direction) comes from gravity. If all the balls are thrown frm a certain height, say x, then:

-The ball thrown horizontally will experience a downward acceleration over a distance of x.

What about the ball thrown vertically? Well, at some point that ball will stop moving upwards and then it will start to move downwards, again because gravity pulls down on it. So we can assume that the ball that is thrown vertically will experience the same downward acceleration, but over a distance >x(do you see why? the ball will start going downwards at a height greater than where it started from, and so acceleration acts upon it for a greater distance).

The ball thrown verically down will have not only a downward pull from gravity, but it will have started at a nonzero downward velocity.

In terms of downwards velocity, the ball initially thrown horizontally (no vertical component initially) will have the lowest downward velocity.

But Ball 1, initially going up, will fall a greater distance, and therefore it will have a longer time to gain downward velocity. On the other hand, ball 3, shot downwards, will already start at a higher downward velocity. You can resolve this by conceptualy understanding that the motion of the upwards-moving object is parabolic, and therefore whatever initial velocity it had (up) will eventually be reflected in the same velocity, but in the opposite direction (what comes up must come down, at the same initial velocity). This means that, in effect, the ball thrown vertically up will eventually have the same vertically downward velocity, which is the same as saying it started out down with the same veocity of Ball 3. It is therefore mathematically the same.

Therefore, the speeds (downward velocity) of Ball 1 and Ball 3 are equal and greater than the speed (downwards velocity) of ball 2.

Answer 2

Ball 1 and Ball 3 will have equal velocities to each other when they hit the ground, and this velocity will be greater than that of the Ball 2.

If you shoot an object upwards, it will reach a maximum height and then fall back down. If we ignore air resistance, then when it falls back down to the release height, it will have a downwards velocity equal in magnitude to its original upwards velocity. That means that Ball 1 will fall back down to the height of the shot location, and it will behave exactly like Ball 3, which was shot down with the same velocity that Ball 1 would also be falling with at that height.

Since Ball 1 and Ball 3 both have downwards velocity at the release height, they will achieve a greater velocity as they hit the ground than will Ball 2, which has a vertical velocity of zero at release.

Answer 3

1&3 have same speed & direction hence they r having same velocity. the speed of ball 2 is same as of 1&2 but its direction is different so its velocity is different.

Answer 4

i) fired horizontally: when it hits the ground, it has a horizontal velocity and vertical velocity gained due to gravity. you have to find theresultant velocity. the path is a parabola
ii)when it is fired downward with a certain velocty , the velocity increases due to gravity before it strikes the ground
iii)when it isbfired vertically upward with a certain velocity,it goes up to the highest point, returns to the point of firing with the same velocity downwards and then the velocty increases due to gravty.