number 14 A ball, thrown downward from the top of a building with an initial spe

Question

number 14

A ball, thrown downward from the top of a building with an initial speed of 3.4, hits the ground with a speed of 23. How tall is the building if the acceleration of gravity is 9.8 and the air resistance is negligible? A stone is thrown upward from the top of a tower, with an initial velocity of 98, Assuming that the height of the tower is 215.6, the acceleration of gravity is 9.8, and the air resistance is negligible, find the maximum height reached by the stone, the time when it passes the top of the tower on its way down, and the total time it has been traveling from launch until it hits the ground. Answers to Odd-Numbered Exercises y(t) = 2 - t^2 - 2t^3. y(t) = t cos t. y(x) = x^2 - 3x + 2. y(x) = (1 - x) ln x. upsilon (t) = 2t, s(t) = t^2 - 4.

Explanation / Answer

u = 98 m/s
v = 0
a = 9.8 m/s^2
v^2 = u^2 - 2*a*s
0 = 98^2 - 2*9.8*s
s = 490 m
Maximum height reached by the stone, including the height of tower = 215.6 + 490 = 705.6 m

v = u - a*t
0 = 98 - 9.8 * t
t = 10 s

Time when it passes the top of the tower , = 2*t = 20 s

s = u*t + 1/2*a*t^2
705.6 = 0 + 1/2 * 9.8 * t^2
t = 12 s

Total travel time since launch, = 12 + 10 = 22 s

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