A stunt man drops from the top of a 50 foot elevator shaft. His height above ground is determined by the equation h=-16(t)(t)+50. At the moment the stunt man begins to drop, an elevator goes up so that its height above ground is determined by the equation h=34t. After how many seconds will the stunt man land on top of the elevator.
I solved using the quadratic equation and obtained an answer of 3.125 seconds or t=-1...is this correct? Thanks!
check your signs. I get
-3.125 or +1
Naturally, the negative answer may be disregarded.
To find the time when the stunt man lands on top of the elevator, we need to set their heights equal to each other and solve for t.
The height of the stunt man above ground is given by the equation h = -16t^2 + 50.
The height of the elevator above ground is given by the equation h = 34t.
Setting these equal to each other, we have -16t^2 + 50 = 34t.
Rearranging the equation, we get -16t^2 - 34t + 50 = 0.
To solve this quadratic equation, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, a = -16, b = -34, and c = 50.
Substituting these values into the quadratic formula, we get t = [ -(-34) ± √((-34)^2 - 4*(-16)*50) ] / (2*(-16)).
Simplifying further, we have t = [34 ± √(1156 + 3200)] / (-32).
Calculating the discriminant, we have √(1156 + 3200) = √4356 = 66.
Therefore, t = [34 ± 66] / (-32).
We now have two possible solutions:
1. t = (34 + 66) / (-32) = 100 / (-32) = -3.125 (approximately -3.125 seconds).
2. t = (34 - 66) / (-32) = -32 / (-32) = 1 (approximately 1 second).
The negative value of -3.125 is not a valid solution in this context, as time cannot be negative.
So, the only valid solution is t = 1 second.
Hence, the stunt man will land on top of the elevator after 1 second.
To determine when the stunt man will land on top of the elevator, we need to find the time at which their heights are equal.
The height of the stunt man is given by the equation h = -16t^2 + 50, and the height of the elevator is h = 34t.
Setting the two equations equal to each other, we have:
-16t^2 + 50 = 34t
Now, rearrange the equation to bring all terms to one side:
-16t^2 - 34t + 50 = 0
To solve this quadratic equation, you can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -16, b = -34, and c = 50. Plugging these values into the formula, we get:
t = (-(-34) ± √((-34)^2 - 4(-16)(50))) / (2(-16))
Simplifying further:
t = (34 ± √(1156 + 3200)) / (-32)
t = (34 ± √(4356)) / (-32)
Since we are looking for a positive time, we can ignore the negative solution:
t = (34 + √(4356)) / (-32)
Calculating the value under the square root:
t = (34 + 66) / (-32)
t = 100 / (-32)
t = -3.125
From the calculations, it appears you made a sign error while evaluating the quadratic equation. The correct value for 't' is -3.125 seconds, which corresponds to a time before the stunt man even starts dropping.
This implies that the stunt man does not land on top of the elevator.