3. Cupid strikes again! This time, he causes Mr. Krabs, SpongeBob\'s boss, to fa

Question

3. Cupid strikes again! This time, he causes Mr. Krabs, SpongeBob's boss, to fall in love with Mrs. Puff Spongebob's teacher at Boating School, on Valentine's Day2. Mr. Krabs gets so excited that he climbs up to the top Krusty Krab, the restaurant that Mr. Krabs owns, and jumps off. According to SpongeBob-lore, the Krusty Krab is an old New England lobster trap. Assuming that the height of the Krusty Krab is 2 feet, Mr. Krab's initial velocity is 4 ft/s, and the acceleration due to gravity is 32 ft/, use htt)so to describe Mr. Krab's equation of motion. (a) What is Mr. Krab's maximum height? (b) At what time does Mr. Krab's hit the ground? (c) With what velocity does Mr. Krab's hit the ground?

Explanation / Answer

h(t) =(-1/2)gt2 +v0t +s0

h(t) = (-1/2) (32) t2 + 4t + 2

h(t) = -16t2 +4t +2

a. h'(t) = -32t + 4

h'(t)=0

-32t+4=0

t= 1/8

h(1/8) = -16(1/8)2+ 4(1/8)+2 =2.25 feet

b. Hit the ground means h (t)=0

-16t2+4t+2=0

8t2-2t-1=0

t =1/2 s

c. v(1/2) = -32(1/2)+4 =-12 ft/s

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