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A train is moving with a constant velocity of 83 m/s in the easterly direction.

A girl on the train looks out the window and sees a boy outside with a toy rocket.

The boy fires the rocket with an initial velocity of 9.8 m/s straight up into the air.

How far does the train travel in the easterly direction while the toy rocket is in the air, i.e. how far does the train travel during the time it takes the rocket to go up and back down to the ground again?

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boffeemadrid

Answer:

166 m

Explanation:

t = Time taken

u = Initial velocity = 9.8 m/s

v = Final velocity

s = Displacement

g = Acceleration due to gravity = 9.80 m/s² = a

Equation of motion

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-9.8}{-9.8}\\\Rightarrow t=1\ s[/tex]

Time taken to go up is 1 second and to go down will also be 1 second

Total time the rocket is up in the air is 2 seconds

[tex]Distance=Speed\times Time[/tex]

[tex]Distance=83\times 2=166\ m[/tex]

The distance the train will travel is 166 m

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