# calculus 2

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A tomato is thrown upward from a bridge 23 m above the ground at 40 m/sec. Take the acceleration of gravity be equal to 9.8 m/s^2

(a) Give formulas for the acceleration, velocity, and height of the tomato at time t.

(b) How high does the tomato go, and when does it reach its highest point?

(c) How long is it in the air?

• calculus 2 -

my equation would be

h = -4.9t^2 + 40t + 23
v = - 9.8t + 40
a = -9.8

b) max h, when v = 0
-9.8t+40=0
t = 40/9 seconds
h= -4.9(40/9)^2 + 40(40/9) + 23 = 103.99 m

c) let's find when it hits the ground, that is, when h = 0
-4.9t^2 + 40t + 23 = 0
4.9t^2 - 40t - 23 = 0
t = (40 ± √2050.8)/9.8
= 8.7 or some negative, which would be silly

It is in the air for appr 8.7 seconds

BTW, that is some feat to throw a tomato about 80 m up into the air !

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