A stunt person falls from a helicopter 609 feet above sea level for an action movie and deploys a parachute when at a height of 500 feet above sea level. The stunt persons height above sea level is defined by the expression 600-16t^2, where t is the time , in minutes, after the fall.
At what time does the stunt person deploy the parachute ?
To find the time at which the stunt person deploys the parachute, we need to set the expression for their height above sea level equal to 500 feet and solve for t:
600 - 16t^2 = 500
Subtracting 500 from both sides:
100 - 16t^2 = 0
Dividing both sides by 16:
- t^2 = -100/16
Simplifying:
t^2 = 25/4
Taking the square root of both sides:
t = ±√(25/4) = ±(5/2)
Since time cannot be negative, we can discard the negative solution, leaving:
t = 5/2
Therefore, the stunt person deploys the parachute at a time of 5/2 minutes, which is equivalent to 2.5 minutes or 2 minutes and 30 seconds.
To find the time at which the stunt person deploys the parachute, we need to solve the equation 600 - 16t^2 = 500.
Subtracting 500 from both sides gives us: 600 - 500 - 16t^2 = 0.
Simplifying the equation further, we have: 100 - 16t^2 = 0.
Next, we can divide both sides by 16: (100 - 16t^2) / 16 = 0 / 16.
This gives us: 100/16 - (16t^2)/16 = 0.
Simplifying further, we get: 6.25 - t^2 = 0.
To solve this quadratic equation, we set it equal to zero and factorize it: (t - 2.5) (t + 2.5) = 0.
This gives us two solutions: t = 2.5 and t = -2.5.
Since time cannot be negative, we can ignore the negative solution.
Therefore, the stunt person deploys the parachute at t = 2.5 minutes after the fall.
To find the time at which the stunt person deploys the parachute, we need to set the expression for their height above sea level, 600-16t^2, equal to 500 and solve for t.
600 - 16t^2 = 500
First, let's subtract 500 from both sides of the equation:
600 - 16t^2 - 500 = 0
Simplifying further:
100 - 16t^2 = 0
Now, we can isolate the variable t by moving 100 to the other side:
-16t^2 = -100
Dividing both sides of the equation by -16:
t^2 = 6.25
To solve for t, we take the square root of both sides:
t = ± √6.25
Now, the square root of 6.25 can be written as ± 2.5.
So, we have two possible values for t: t = 2.5 or t = -2.5.
Since time cannot be negative in this context, we can conclude that the stunt person deployed the parachute at t = 2.5 minutes after the fall.