An object thrown vertically upwards (on Earth) with a velocity of v0 ft/s from a

Question

An object thrown vertically upwards (on Earth) with a velocity of v0 ft/s from a height of h0 ft has height h(t) = ?16t 2 + v0t + h0 ft at time t seconds. (a) Nolan Ryan, one of the fastest baseball pitchers of all time, was capable of throwing a baseball 150 ft/s (over 102 mi/h). During his career, he had the opportunity to pitch in the Houston Astrodome. The Astrodome was an indoor stadium with a ceiling 208 ft high. Could Nolan Ryan have hit the ceiling of the Astrodome if he were capable of giving the baseball an upward velocity of 100 ft/s from a height of 7 ft? (b) How fast would Nolan Ryan have to throw a ball upward from a height of 7 ft in order to hit the ceiling of the Astrodome?

Explanation / Answer

h(t) =-16t 2 + v0t + h0

inorder to reach the cieling the h(t) should be = 208 ft

208 = %u221216t 2 + 100t + 7

or , 16t^2 -100t + 201 = 0

t^2 - 6.25t + 12.56 = 0

root s = 6.25 +- sqrt( 6.25^2 - 4 x 12.56) / 2

= the rooths are imaginary

thus he canoot hit the ceiling with 100 ft/s

now

part 2

208 =-16t 2 + vt + 7

16t^2 -v x t + 201 = 0

for time to be real the discriminanat needs to be positive or zero

b^2 - 4ac >=0

v^2 - 4 x 201 x 16 >= 0

v^2 >= 113.419 ft/s

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