# How Fast Was the Second Stone Thrown to Match the First at the Cliff Base?

• Ab17
In summary, The first stone is dropped from a cliff at a height of 200 meters and the second stone is thrown up at a velocity of 16.94 meters per second.
Ab17

## Homework Statement

a stone is dropped from a cliff 200m high.if a second stone is thrown verticall upwards 1.50seconds after the first was released.strike the cliff base at the same instant as the first stone.with what
velocity was the second stone thrown

2. Homework Equations

Xf=xi +vt + 0.5t^2

Vf= vi + at

## The Attempt at a Solution

The First Stone.

d1 = -0.5g*t^2 = -4.9*(1.5)^2 = -11 m. =

Distance traveled by 1st stone after 1,5s. Vf= Vi+at.

Vf= 0 -9.8*1.5 = -14.7m/s

V = -14.7 m/s = Velocity of 1st stone after 1.5 s.
d1 = Vo*t + 0.5g*t^2

-200 = -11 - 14.7 t -4.9t^2

-4.9t^2 -14.7t +189=0

Tf = 4.89 s. = Fall time or time for each stone to reach Gnd. The 2nd Stone.

d = Vo*t + 0.5g*t^2 = -200 m.

Vo*4.89 -4.9*(4.89)^2 = -200

Vo= -16.94m/sWhy Am I getting a negative answer the upward velocity should be positive (the top of the cliff is taking as the X=0 position)

Ab17 said:
d1 = Vo*t + 0.5g*t^2

-200 = -11 - 14.7 t -4.9t^2

-4.9t^2 -14.7t +189=0

Tf = 4.89 s. = Fall time or time for each stone to reach Gnd.The 2nd Stone.

d = Vo*t + 0.5g*t^2 = -200 m.

Vo*4.89 -4.9*(4.89)^2 = -200

Vo= -16.94m/sWhy Am I getting a negative answer the upward velocity should be positive (the top of the cliff is taking as the X=0 position)

i think you should check your calculation ...
if the time taken by the 2nd stone to go up and come down is known then it should be equal to 2.V0/g as a body being sent up will come to rest after a time V0/g and fall on ground taking same time.
taking

Ab17 said:
a stone is dropped from a cliff 200m high.if a second stone is thrown verticall upwards 1.50seconds after the first was released.strike the cliff base at the same instant as the first stone.with what
velocity was the second stone thrown
try to think on the event
1. the 1st. stone is falling through height h so one can calculate time taken say t1 easily using distance traversed.
2. after 1st. one is dropped the second has been thrown up say after 1.5 sec.
3. time of flight of second stone can be easily computed as function of initial velocity of throw.
the above time of flight can be related.

## 1. What is free fall?

Free fall is the motion of an object under the influence of gravity, without any other forces acting on it. This means that the object is only accelerating due to the pull of gravity, and is not being slowed down or sped up by any external forces.

## 2. How does the acceleration of an object in free fall compare to the acceleration due to gravity?

The acceleration of an object in free fall is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth. This means that an object in free fall will accelerate at a constant rate towards the ground until it reaches terminal velocity.

## 3. What is the formula for calculating the distance an object in free fall has fallen?

The formula for calculating the distance an object in free fall has fallen is d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time in seconds.

## 4. How does the mass of an object affect its rate of free fall?

The mass of an object does not affect its rate of free fall. All objects, regardless of their mass, accelerate at the same rate due to gravity. This was famously demonstrated by Galileo when he dropped objects of different masses from the Leaning Tower of Pisa.

## 5. What is terminal velocity and how does it relate to free fall?

Terminal velocity is the maximum speed that an object can reach while falling through a fluid, such as air or water. In free fall, an object will continue to accelerate until it reaches terminal velocity, at which point the forces of gravity and air resistance are balanced and the object will fall at a constant speed.

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