DofotheroU

2021-08-11

Alpinists reach a ledge that is 20 ft above. The height (in feet) is given by the function $h=-16{t}^{2}+32t+5$ , where t is the time that the hook is in the air (in seconds). Can they throw it high enough to reach the ledge? What time (in seconds) will it take for the hook to reach the maximum height?

crocolylec

Skilled2021-08-12Added 100 answers

a<0, so the maximum occurs at:

Substitute to find what is the t for the maximum:

Substitute for maximum height:

It will 1 second for the hook to reach its max height, which is 21ft. Since the ledge is 20 ft high and 21>20, they can throw it high enough.

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