You helped me with this question earlier today, the answer you got was incorrect, i tried looking through your calculations but i cant find the mistake. the program wont let me see the right answer just tells the answer i put in was wrong. can you please look over it again thank you
Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910m in Yosemite National Park. Assume a jumper runs horizontally off the top of El Capitan with speed 5.0m/s and enjoys a freefall until she is 150m above the valley floor, at which time she opens her parachute .
Q: how long is the jumper in freefall? ignore air resistance
Without air resistance, the horizontal velocity does not matter.
The free fall is over a vertical distance of 150-910=-760m
S=v0t-(1/2)gt² where v0=0
t=sqrt(-2S/g)
=sqrt(2*760/9.81)
=12.45 s.
h=H-H(o) =910-150 =760 m/s
h=g•t^2/2,
t=sqrt(2•h/g) = sqrt(2•760/9.8)=
=sqrt (155)=12.45 s.
thank you.
To calculate the time the jumper is in freefall, we need to use the equations of motion. We'll assume that the positive direction is upward, and the initial position is at the top of El Capitan.
We can start by finding the time it takes for the jumper to reach the point where she opens her parachute. We know the initial velocity (speed) of the jumper is 5.0 m/s, and the acceleration due to gravity is about 9.8 m/s².
Using the kinematic equation:
Δy = v₀t + (1/2)at²
Where:
Δy = vertical displacement (150 m)
v₀ = initial velocity (5.0 m/s)
a = acceleration due to gravity (-9.8 m/s²)
t = time
Plugging in the known values, we can solve for t:
150 = (5.0)t + (1/2)(-9.8)t²
150 = 5.0t - 4.9t²
4.9t² - 5.0t + 150 = 0
Now, to solve for t, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 4.9, b = -5.0, and c = 150. Plugging in these values, we get:
t = (-(-5.0) ± √((-5.0)² - 4(4.9)(150))) / (2(4.9))
Simplifying further will give us the values of t.