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Freefall & Motion

A stone is th...

Question

A stone is thrown vertically upwards with a velocity odf 19.6m/s. After 2s another stone is thrown upwards with a velocity of 9.8m/s. When and where will the two stones collide??

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Solution

$F o r t h e f i r s t s t o n e, i n i t i a l v e l o c i t y = 19.6 m / s t i m e t a k e n t o r e a c h h e i g h e s t p o i n t i s t v = u + a t 0 = 19.6 - 9.8 t t = 2 s m a x i m u m h e i g h t h h = u t + \frac{1}{2} a t^{2} h = 19.6 \times 2 - 0.5 \times 9.8 \times 4 h = 19.6 m w h e n f i r s t s t o n e i s a t t h e t o p m o s t p o i n t t h e n s e c o n d s t o n e i s t h r o w n . l e t x i s t h e d i s \tan c e t r a v e l l e d w h e r e t h e y m e e t i n t i m e t_{1} x = \frac{1}{2} g {t_{1}}^{2} f o r s e c o n d s t o n e d i s \tan c e t r a v e l l e d i s h - x h - x = 9.8 t_{1} + 0.5 \times 9.8 \times {t_{1}}^{2} o n s o l v i n g t h e s e t w o e q u a t i o n s w e g e t t_{1} = 2 s a n d x = 19.6 m s o t h e s e t w o s t o n e s m e e t a t g r o u n d a f t e r 2 + 2 = 4 s .$

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