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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
A car starts from rest and accelerates uniformly with 2 m/s2. At t = 5s a stone is dropped out of the window 15 m high of the car. What is velocity and acceleration of stone at t = 5·5 s? ( g = 10m/s2).

Given, 

Car starts from rest. That is, 

Initial velocity = 0 m/s
Uniform acceleration of the car = 2 m/s2
Velocity of car at t = 5s =  10 m/s

            

When stone is dropped, the velocity of car and hence velocity of stone is 10 m/s in horizontal direction.

Since at 5s the stone loses the contact from car, therefore, the stone will move uniformly in horizontal direction and accelerate in vertically downward direction due to gravity.

At t = 5·5s or 0·5 s after the stone is dropped, the X and Y component of velocity are 

straight V subscript straight x space equals space straight v subscript straight x space plus space straight a subscript straight x space straight t space equals space 10 space plus space 0 cross times 0.5 space equals space 10 space straight m divided by straight s

straight V subscript straight y space equals space straight v subscript straight y space plus space straight a subscript straight y straight t space equals space 0 space plus space 10 cross times 0.5 space equals space 5 space straight m divided by straight s space
 

So, magnitude of velocity is given by, 

straight V space equals space square root of straight V subscript straight x squared plus straight V subscript straight v squared end root space equals space square root of 10 squared plus 5 squared end root space equals space 5 square root of 5 space straight m divided by straight s

Acceleration of the stone at t=5.5 sec is the same as acceleration due to gravity. 

That is, acceleration = 10 m/s2 

And, 

Angle of inclination with the horizontal, straight theta = straight v subscript straight y over straight v subscript straight x space equals space 1 half

i.e., straight theta space equals space 26 to the power of straight o space 33 to the power of apostrophe

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