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 2003-18-06-00-00_files/i0030000.jpg, 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

Option B: 1.6 s.

Although the equation is not included, you can obtain it by physical considerations

H(t) = -16.t^2 + 52t + 16

The maximum point is at the vertex and the vertex is in the middle of the roots.

The roots are when H(t) = 0,

So you have to solve 0 =-16t^2 + 52t + 16

Use the quadratic formula and you will find t = 3.53 and t =-0.28

Then the vertex is at the middle point = (3.53 -.028)/2 =1.63 s and the answer is option B: 1.6 s.