A bungee jumper leaps from the top of a building that is 420 feet tall and falls at an average rate of 95 feet per second. at the time of the jump, the elevator is at a height of 130 feet and rising at a rate of 3.6 feet per second. about how many seconds will pass until the jumper and the elevator are at the same height.
The time is the same, the place is the same.
The person falls x feet (95t),so its position is 420 - 95t; the elevator rises to (130+3.6t).
Set the places equal..
420 - 95t= 130 + 3.6 t
solve for time.
check my thinking
okay thanks that helped a bunch.. how would you solve for the height they'll meet at in that same equation?
Well, to solve for the height at which they will meet, you would substitute the value of t (the time) into either one of the expressions for the height. Since we already have one expression for the height of the jumper, let's use that.
So, the height of the jumper at the time t is given by 420 - 95t. Now, we just need to calculate the height at that specific time. Let's substitute t into the equation:
Height of the jumper at time t = 420 - 95t
Let's say we solve for t and find that t = 5 seconds. Now, we can substitute this value of t back into the expression for the height of the jumper:
Height of the jumper at time t = 420 - 95t
Height of the jumper at time 5s = 420 - 95 * 5
Height of the jumper at time 5s = 420 - 475
Height of the jumper at time 5s = -55 feet
Therefore, the jumper and the elevator would meet at a height of -55 feet. Keep in mind that this negative sign indicates that the height is below ground level. Since it doesn't make sense for them to be below ground level, it's possible that my calculations are incorrect or that I misunderstood something.
To solve for the height at which the jumper and the elevator will meet, you need to solve the equation:
420 - 95t = 130 + 3.6t
First, combine like terms by adding 95t and subtracting 130 from both sides of the equation:
290 = 98.6t
Next, divide both sides of the equation by 98.6 to isolate t:
t ≈ 2.943 seconds
To find the height at which they will meet, substitute this value of t back into either of the original equations. Let's use the equation for the jumper's position:
Jumper's position at time t = 420 - 95t
Jumper's position at time t ≈ 420 - 95(2.943)
≈ 420 - 279.885
≈ 140.115 feet
Therefore, the jumper and the elevator will meet at a height of approximately 140.115 feet.
To solve for the height at which the jumper and the elevator will meet, we need to set their positions equal to each other and solve for the height.
The position of the jumper is given by the equation: 420 - 95t.
The position of the elevator is given by the equation: 130 + 3.6t.
Setting these two equations equal to each other, we can solve for t:
420 - 95t = 130 + 3.6t
Combining like terms:
95t + 3.6t = 420 - 130
98.6t = 290
Dividing both sides by 98.6:
t = 290 / 98.6
Solving this, we find that t is approximately 2.94 seconds.
To find the height at which they will meet, we can substitute this value of t into either of the original equations.
For example, substituting t = 2.94 into the equation for the jumper's position:
Height = 420 - 95t
Height = 420 - 95 * 2.94
Height = 420 - 279.3
Height ≈ 140.7 feet
Therefore, the jumper and the elevator will meet at a height of approximately 140.7 feet above the ground.