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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

Verified Answer :

Edufirst

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.

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