Read the following word problem and solve as necessary Micha

Read the following word problem and solve, as necessary. Michael went on a mission trip to Costa Rica, and he found some time to go search for adventure. He and some friends went zip-lining down a volcano and cliff diving. When Michael jumped off the cliff into the ocean, his height (in feet) above the water could be modeled by the equation h = -16t^2 + 16t + 480, where h is his height and t is the times in second since he jumped. A. How high is the cliff above the water? Meaning, how high was Michael above the water right before he jumped off the cliff? and explain your thought process. B. How many second did it take Michael to hit the water?

Solution

A. We have h = -16t² +16t +480, whereh is the height and t is the time in seconds since Michael jumped off the cliff. Thus, when t = 0, we have h = 480 ft. Thus, Michael was 480 ft. above the water when he jumped.

B. Michael jumped off the cliff when he was 480 ft. above the water. Let us assume that Michael hits water t seconds after he jumped off the cliff. Since h = 0 when he hits the water, we have 0 =-16t² +16t +480 or,16t²-16t -480 =0. On dividing both the sides by 16, we get t² -t -30 = 0 or, t² -6t+5t -30= 0 or, t(t-6)+5(t-6) = 0 or, (t-6)(t+5) = 0. Since t cannot be negative, we have t = 6. Hence, Michael hits water 6 seconds after he jumped off the cliff.