Question

A model jet is fired up in the air from a 16-foot platform with an initial upward velocity of 52 feet per second. The height of the jet above ground after t seconds is given by the equation h=-16t^2+52t+16, where h is the height of the jet in feet and t is the time in seconds since it is launched. Approximately how long does it take the jet to reach its highest point?

a. 0.3 seconds
b. 1.6 seconds
c. 3.3 seconds
d. 6.5 seconds

Answer 1

Answer: option B

h=-16
`t^(2)`+52t+16

where h is the height of the jet in feet and t is the time in seconds since it is launched.

We need to find the time taken to reach the maximum height.

Highest point is the vertex of the given equation.

To find the x coordinate of vertex we use a formula

t =
`(-b)/(2a)`

From the given equation

h=-16
`t^(2)`+52t+16

a= -16 , b= 52, c= 16

Plug in the values in the formula

t =
`(-b)/(2a)`

t =
`(-52)/(2*(-16))`

t= 1.625 seconds

Approximately t= 1.6 seconds