# calculus

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an object is fired upward at the end of the burn it has an upward velocity of 245m/s and is 14.7 m high
a) find the maximum height and when it is attained
b) when it reaches the ground

i know that i have to use the quadratic function s= -4.9t²+Vot+h

but for what i have the 4.9t² how can i use it and can help me with the problem please

• calculus -

For the max height, energy thinking
top PEnergy = intial PE + Initial Kenergy
mgh=mg*14.7 + 1/2 m 245^2
solve for h, the maximum height.

when is it attained?
h=14.5+245t -1/2 g t^2 for h max, solve for time t.
when it reaches the ground?
h=0 solve for time.

• calculus -

The 4.9 is a fixed constant and deals with the force of gravity on earth.

s = -4.9t^2 + 245t + 14.7

take the derivative set it equal to zero and solve for t
put that t back into the equation to find the maximum height

b) when it hits the ground, s = 0
so solve 0 = -4.9t^2 + 245t + 14.7 for t

• calculus -

great job

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