Question 348743: A flare is shot upwards from the deck of a ship. The initial upward velocity of the flare is 30m/s and the deck is 10m above the surface of the ocean. The height of the flare in metres is given by h=-5t^2 +30t+10, where t is in seconds.
a)determine the average velocity of the flare during each of its first 6 seconds?
b)why does the velocity change from positive to negative?
c)when will the flare reach its maximum height?
d)determine the instantaneous velocity of the flare at t=3 seconds by using slopes of secants.
e)What is the significance of your answer to d.
Can one of the tutors please help me with this question. Thank You!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
a) Substitute the values, 0, 1, 2, 3, 4, 5, 6 for t in the function and do the arithmetic to get the height at each of those times. Subtract the value at zero seconds from each value, and divide by the number of seconds.
b) Upward velocity is positive, downward velocity is negative. What goes up, must come down.
c) The graph of the function is a parabola. Use  to calculate the  -coordinate of the vertex of the parabola.
d) Plot the points for t = 2 and t = 4. Find the slope of the line through )) and )) . The slope of that secant will be the value of the instantaneous velocity at t = 3.
e) That's where the flare stops going up and starts back down again.
You will do better if you consider this as a formula for height of a projectile as a function of  , namely: \ =\ -4.9t^2\ +\ v_ot\ +\ h_o) .
John
My calculator said it, I believe it, that settles it
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