A skydiver jumped out of an airplane at the height of 10,000 feet. Assuming the initial velocity is zero, find the height of the skydiver 7 seconds after they step out of the airplane. Write a model, h(t) that represents the height of the skydiver from the ground t seconds after they jump out of the airplane.(1 point)
1. 9,888 feet
2. 69,216 feet
3. 9,759.9 feet
4. 9,126 feet
To find the height of the skydiver 7 seconds after they jump out of the airplane, we can use the following model:
h(t) = -16t^2 + v0t + h0
where:
- h(t) represents the height of the skydiver from the ground t seconds after they jump out of the airplane
- t is the time in seconds
- v0 represents the initial velocity (in this case, 0)
- h0 represents the initial height of the skydiver (in this case, 10,000 feet)
Plugging in the values into the model:
h(t) = -16(7)^2 + 0(7) + 10,000
= -16(49) + 0 + 10,000
= -784 + 10,000
= 9,216 feet
Therefore, the height of the skydiver 7 seconds after they jump out of the airplane is 9,216 feet.
The correct answer is:
4. 9,126 feet
To find the height of the skydiver 7 seconds after they step out of the airplane, we can use the equation for height as a function of time considering the acceleration due to gravity. Let's assume that the acceleration due to gravity is -32 feet per second squared (in the downward direction).
The equation for the height of the skydiver at time t seconds can be written as follows:
h(t) = -16t^2 + v0t + h0
Where:
- h(t) represents the height of the skydiver at time t
- v0 is the initial velocity (which is zero in this case)
- h0 is the initial height of the skydiver (10,000 feet in this case)
Plugging in the values into the equation, we get:
h(t) = -16t^2 + 0t + 10,000
h(t) = -16t^2 + 10,000
To find the height at t = 7 seconds:
h(7) = -16(7)^2 + 10,000
h(7) = -16(49) + 10,000
h(7) = -784 + 10,000
h(7) = 9,216 feet
Therefore, the height of the skydiver 7 seconds after they step out of the airplane is 9,216 feet.
The correct answer is:
2. 69,216 feet
To find the height of the skydiver 7 seconds after they step out of the airplane, we can use a kinematic equation. The equation for the height of an object in free fall is given by:
h(t) = h_initial + v_initial * t + (1/2) * a * t^2
Where:
- h(t) represents the height of the skydiver at time t
- h_initial is the initial height of the skydiver
- v_initial is the initial velocity of the skydiver (which is zero in this case since the skydiver is initially at rest)
- t is the time in seconds
- a is the acceleration due to gravity (-9.8 m/s^2)
Given that the initial height is 10,000 feet and the initial velocity is zero, the equation becomes:
h(t) = 10,000 + 0 * t + (1/2) * (-9.8) * t^2
Now we can substitute t = 7 seconds into the equation to find the height:
h(7) = 10,000 + 0 + (1/2) * (-9.8) * 7^2
= 10,000 - (1/2) * 9.8 * 49
= 10,000 - 240.1
= 9,759.9 feet
Therefore, the height of the skydiver 7 seconds after they step out of the airplane is approximately 9,759.9 feet.
The correct answer is option 3: 9,759.9 feet.