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A 10mlong glider with a mass of 680kg(including the passengers) is gliding horizontally through the air at when a 60kgskydiver drops out by releasing his grip on the glider. What is the glider鈥檚 velocity just after the skydiver lets go?

Short Answer

Expert verified

The velocity of the glider just after the skydiver lets go isvf=30m/s.

Step by step solution

01

Given information  

We need to find the velocity of the glider just after the skydiver lets go .

02

Simplify 

When the initial momentum equals the final momentum, the momentum of an isolated system changes to zero. The particle interactions are isolated from the external environment. Because momentum is conserved, we apply the law of conservation of momentum, which is given by equation in the form

Pf=Pi(1)

Because of isolated system the railway is frictionless. The object has mass mand moves with speed vthat has momentum p, Vector is a product of object's mass and its velocity.The momentum is given by equation in the form

p=mv(2)

Glider's initial velocity is vi=30m/sand total initial mass is mi=680kg. To get initial momentum pi

pi=mivi=680kg30m/s=(20400kg)(m/s)

The final mass of glider after skydiver drops out is

mf=680kg-60kg=620kg

03

Simplify 

Skydivers gain the velocity of gliders, so our final system is a combination of gliders and skydivers. To calculate the final momentum,

pf=mfvf+mskydivervskydiver=620kgvf+60kg30m/s=620kgvf+1800

To get the equation for vf, put the expression into equation (1)

pi=620kgvf+1800vf=pi-1800620kg(3)

After putting values for piinto equation 3to get vf

vf=pi-1800620kg=(20400kg)(m/s)-1800620kg=30m/s

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