Question

A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.
A - 2 seconds

B - 10 seconds

C - 12 seconds

D - 5 seconds

Answer 1

When the rocket reaches the platform, then h must be equal to 0

h=0

Calculating for t using the equation:

h=-t^2+3t+10

0 = -t^2+3t+10
reversing sides: 
t^2 -3t -10 = 0 

By completing the squares or factoring, we can get the roots: 

(t-5)(t+2) =0 
t=5 or t=-2 

Since time cannot be negative, therefore: 

t = 5 seconds 

Answer is D.

Answer 2

Answer:

D - 5 seconds

Step-by-step explanation:

Set h equal to zero, then reverse the equation:

$t^{2} - 3t - 10 = 0 \\ \\ (t + 2)(t - 5) = 0 \\ - 2 = t \: \: \: 5 = t$

Since time is NEVER negative, we take the five seconds.

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