Tarzan swings on a 26.2 m long vine initially inclined at an angle of 39° from the vertical.
(a) What is his speed at the bottom of the swing if he starts from rest?
(b) What is his speed at the bottom of the swing if he starts with an initial speed of 3.26 m/s?
(a) Think consewervation of energy
M*g*H = (1/2) M V^2
V = sqrt(2 g H)
H is the elevation decrease.
H = 26.2 (1 - cos39) = 5.84 m
(b) M g H = CHANGE in kinetic energy
g*H = (1/2)[V^2 - 3.26^2]
Solve for V
This assumes that Tarzan's initial velocity is along the arc of motion of the swing. There could be some small change if it isn't.
where did you get the 3.26 in part b? i don't understand that part really...i get the first part though
im sorry im having a off day, i see it now
Good
wait what would the answer be to part b im not getting the right answer
Where did u get 5.84m
To answer these questions, we need to use the principles of energy conservation. The total mechanical energy at any point during the swing of Tarzan is the sum of the potential energy and the kinetic energy.
Let's start by finding the potential energy at the highest point of the swing. The potential energy is given by the equation:
PE = mgh
Where m is the mass of Tarzan, g is the acceleration due to gravity, and h is the height above the lowest point (the bottom of the swing).
(a) If Tarzan starts from rest, his initial potential energy is maximum, and kinetic energy is zero. So, at the bottom of the swing, all the potential energy will be converted to kinetic energy.
Kinetic energy is given by the equation:
KE = (1/2)mv^2
Where v is the velocity at the bottom of the swing.
Using the conservation of energy:
PE_top = KE_bottom
mgh = (1/2)mv^2
We can cancel out the mass term on both sides:
gh = (1/2)v^2
Rearranging the equation, we can solve for v:
v = sqrt(2gh)
Substituting the known values:
g = 9.8 m/s^2 (acceleration due to gravity)
h = 26.2 m (length of the vine)
v = sqrt(2 * 9.8 m/s^2 * 26.2 m)
Calculate the expression and you will get the answer for Tarzan's speed at the bottom of the swing.
(b) If Tarzan starts with an initial speed of 3.26 m/s, we need to consider both the initial kinetic energy and the potential energy.
Using the conservation of energy:
PE_top + KE_initial = KE_bottom
mgh + (1/2)mv_initial^2 = (1/2)mv^2
Again, we can cancel out the mass term:
gh + (1/2)v_initial^2 = (1/2)v^2
Rearranging the equation, we can solve for v:
v = sqrt(2 * (gh + v_initial^2/2))
Substituting the known values:
g = 9.8 m/s^2 (acceleration due to gravity)
h = 26.2 m (length of the vine)
v_initial = 3.26 m/s (initial speed)
v = sqrt(2 * (9.8 m/s^2 * 26.2 m + (3.26 m/s)^2/2))
Calculate the expression and you will get the answer for Tarzan's speed at the bottom of the swing when he starts with an initial speed of 3.26 m/s.