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Marina86 [1]
3 years ago
8

The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t,

where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.
Mathematics
1 answer:
AleksAgata [21]3 years ago
4 0

Answer:

7.5 seconds

Step-by-step explanation:

h =  - 16 {t}^{2}  + 120t \\  \because \:  we \: have \: to \: find \:  the  \:  time  \: required  \:  \\ for \:  the \:  object \:  to \:  return to \:  its  \:  \\ point \:  of  departure. \\  \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\  \therefore \: 0 =   - 16 {t}^{2}  + 120t \\ \therefore \:16 {t}^{2}  - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \:  \: or \:  \: (2t - 15) = 0 \\ \therefore \:t =  \frac{0}{8}  \: or \: t =  \frac{15}{2}  \\ \therefore \:t = 0 \: or \: t = 7.5 \\  \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{  \therefore \: t = 7.5 \: seconds}}

Thus, the time required for the object to return to its point of departure is 7.5 seconds.

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