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)
Responses
9,126 feet
9,126 feet
69,216 feet
69,216 feet
9,888 feet
9,888 feet
9,759.9 feet
To find the height of the skydiver 7 seconds after they step out of the airplane, we can assume that the only force acting on the skydiver is gravity. The equation that relates height, initial velocity, time, and acceleration (due to gravity) is given by:
h(t) = -16t^2 + vt + h0
Where:
- h(t) is the height of the skydiver at time t,
- 16 is half of the acceleration due to gravity (32 ft/s^2),
- t is the time in seconds,
- v is the initial velocity (which is zero in this case),
- h0 is the initial height (10,000 feet).
Plugging in the values into the equation:
h(7) = -16(7)^2 + 0(7) + 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.
To find the height of the skydiver 7 seconds after they step out of the airplane, we can use the equation of motion for free fall:
h(t) = -16t^2 + vt + h
where:
h(t) is the height of the skydiver from the ground at time t,
t is the time in seconds,
v is the initial velocity of the skydiver (which is zero since they have no initial velocity),
and h is the initial height of the skydiver (which is 10,000 feet).
Substituting the given values into the equation, we have:
h(t) = -16(7)^2 + 0(7) + 10,000
Simplifying:
h(t) = -16(49) + 10,000
h(t) = -784 + 10,000
h(t) = 9,216 feet
Therefore, the height of the skydiver 7 seconds after they step out of the airplane is 9,216 feet.
To find the height of the skydiver at a particular time, you can use a mathematical model that represents the height of the skydiver as a function of time.
Let's assume that the skydiver experiences the force of gravity but no other forces like air resistance. In that case, the equation for the skydiver's height, h(t), can be represented using kinematic equations:
h(t) = h0 - (1/2)gt^2
Where:
h(t) is the height of the skydiver at time t
h0 is the initial height (10,000 feet in this case)
g is the acceleration due to gravity (approximately 32.2 feet per second squared)
To find the height of the skydiver 7 seconds after stepping out of the airplane, substitute t = 7 into the equation:
h(7) = 10,000 - (1/2)(32.2)(7)^2
h(7) = 10,000 - (1/2)(32.2)(49)
h(7) = 10,000 - (16.1)(49)
h(7) = 10,000 - 789.9
h(7) ≈ 9,210.1 feet
Therefore, the height of the skydiver 7 seconds after stepping out of the airplane is approximately 9,210.1 feet.