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Algebra
Pregunta

A missile is fired vertically upward such that its...

A missile is fired vertically upward such that its distance, \( s \) (in metres), above the ground is given by. 

\( s = 50 + 90 t - 4.9 t ^ { 2 } , \) 

where t is time (in seconds). (a) When will the missile hit the ground? (b) What is the maximum height of the missile? 

Answer

a) When the missile hits the ground, s = 0

So, quadratic equation will be 

-4.9t^2 + 90 t + 50 = 0

t = ( -90 \(\pm\)\(\sqrt{90^2 - 4 (- 4.9) (50)}\)  ) / 2 * -4.9

 

On solving the above, we get t = 18.907 seconds

 

 

b) For max. height, differentiate 's' w.r.t t and equate to 0

\(\dot{s}\) = -9.8 t + 90 = 0

t = 90 /9.8 = 9.183

Max height occurs at t = 9.183 seconds

 

So s at t = 9.183 

Max height = s(9.183)= 50 + 90  9.183 -  4.9 (9.183^2)

Max. Height = 463.325 metres

 

Solución
View full explanation on CameraMath App.