Question

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.

Answer 1

7.5 seconds

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 = (0)/(8) \: or \: t = (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.