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A ball is thrown vertically upward with an initial speed of 20m/s. Two second later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24m/s. At what height above the release point will the ball and stone pass each other?
After just over three and a quarter seconds.
Time taken: 4.06 seconds.Final velocity: 42.8 m per sec.
Yes it can, and it's really easy. -- A stone tossed upward, before it peaks and starts falling, has upward velocity and downward acceleration. -- A car driving east and slowing for a stop-sign has eastward velocity and westward acceleration.
Of course. Toss a stone straight up. -- From the moment it leaves your hand until the moment it hits the ground, it has constant acceleration ... the acceleration of gravity, around 10 meters per second2. The number isn't important, only the fact that the acceleration of the stone is not zero until it hits the ground. -- Velocity-wise: The stone starts out with some upward velocity, which steadily decreases until it's at the top of its arc, then the velocity becomes downward and increases until the stone hits the ground. -- At the very top of the arc, there is a point where the velocity changes from upward to downward. In order for that to happen, there must be an instant when the velocity is zero. -- But the acceleration is constant and not zero, even at that instant when the velocity is zero.
A ball is thrown vertically upward with an initial speed of 20m/s. Two second later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24m/s. At what height above the release point will the ball and stone pass each other?
After just over three and a quarter seconds.
v2 = u2 + 2as where v = current velocity, u = initial velocity, a = acceleration, and s = displacement. Taking a = - 9.8 ms-2 v2 = 182 - (9.8 x 11 x 2) = 108.4 v = 10.4 ms-1
Time taken: 4.06 seconds.Final velocity: 42.8 m per sec.
Yes it can, and it's really easy. -- A stone tossed upward, before it peaks and starts falling, has upward velocity and downward acceleration. -- A car driving east and slowing for a stop-sign has eastward velocity and westward acceleration.
Of course. Toss a stone straight up. -- From the moment it leaves your hand until the moment it hits the ground, it has constant acceleration ... the acceleration of gravity, around 10 meters per second2. The number isn't important, only the fact that the acceleration of the stone is not zero until it hits the ground. -- Velocity-wise: The stone starts out with some upward velocity, which steadily decreases until it's at the top of its arc, then the velocity becomes downward and increases until the stone hits the ground. -- At the very top of the arc, there is a point where the velocity changes from upward to downward. In order for that to happen, there must be an instant when the velocity is zero. -- But the acceleration is constant and not zero, even at that instant when the velocity is zero.
Throwing a stone from a moving train involves the same type of calculations as throwing a stone from a stationary platform. The difference is that you now consider the added horizontal velocity imparted by the moving train. If you throw forward, the train's velocity is added to your contribution to the stone. If you throw backward, the train's velocity is subtracted from your contribution to the stone. If you throw sideways, the train's velocity does not alter your contribution to the stone. Whether any of this matters or not depends on friction due to the different air velocities encountered by the stone. Vertical velocity is relatively unchanged by the train's contribution. The stone will still go up (if you include an upward vector in your throw) and it will still go down. The end result is that the stone will hit the ground at some point. That point will be relatively the same in both cases, except for the minor difference due to air velocity.
The vertical component of its velocity increases at the rate of 9.8 meters (32.2 feet) per second downward every second. Without involving numbers, simply the vertical component will first be upward at what ever velocity it is when split from the horizontal velocity, then (after reaching the peak of its height at which velocity is zero) it will be a downward vector that, yes, will increase with acceleration due to gravity (which is where the 9.8 meters per second squared came from)
Of course. Anything you toss with your hand has constant acceleration after you toss it ... the acceleration of gravity, directed downward. If you toss it upward, it starts out with upward velocity, which reverses and eventually becomes downward velocity.
How far? In absence of air resistance, distance will be 24.522 meters (rounded). The max. range that will be achieved will depend on how much faster you can throw that stone but for 16m/sec initial velocity it will only reach 24.522m at 35 degr. launch angle.
If you ignore the effect of the air grabbing at it and only figure in gravity, then the horizontal component of velocity is constant, from the time the stone leaves your hand until the time it hits the ground. Makes no difference whether you toss it up, down, horizontal, or on a slant. Also makes no difference whether it's a cannonball, a stone, or a bullet.
both the magnitudes and the directions of the initial and final velocities are the same.