Tarzan (m = 68kg) swings down from a height of 4.8m on a vine to save Jane (m = 35kg) from some hungry hippos. if he gravs jane in an inelastic collision at the bottom of the vine's path, how high will they swing up to after the collision?
m₁gh₁ =mv²/2,
v=sqrt(2gh₁)=…
m₁v=(m₁+m₂)u,
u= m₁v/(m₁+m₂)=..
.
(m₁+m₂)u²/2=(m₁+m₂)gh₂,
h₂=(m₁+m₂)u²/2(m₁+m₂)=..
To solve this problem, we can use the principle of conservation of mechanical energy. In an inelastic collision, momentum is conserved, but some energy is lost as they stick together.
First, let's calculate the initial potential energy of Tarzan when he is at a height of 4.8m. The formula for potential energy is:
Potential Energy = mass x gravity x height
Using the mass of Tarzan (m = 68kg), the acceleration due to gravity (g = 9.8m/s²), and the height (h = 4.8m), we can calculate the potential energy:
Potential Energy of Tarzan = 68kg x 9.8m/s² x 4.8m
Next, let's calculate the initial potential energy of Jane when she is at the same height. Using the given mass of Jane (m = 35kg) and the same height:
Potential Energy of Jane = 35kg x 9.8m/s² x 4.8m
Since Tarzan and Jane are initially at rest, their initial kinetic energy is zero.
Now, after the collision, Tarzan and Jane will swing up to a new height. Let's call that height h2.
At that height, the total mechanical energy (potential energy + kinetic energy) will be equal to the initial mechanical energy.
Total Mechanical Energy = Potential Energy of Tarzan + Potential Energy of Jane
Total Mechanical Energy = (68kg x 9.8m/s² x 4.8m) + (35kg x 9.8m/s² x 4.8m)
Now, we need to find the corresponding height (h2) at which the mechanical energy is conserved. Rearranging the equation for potential energy:
Potential Energy = mass x gravity x height
We can solve for h2:
h2 = (Total Mechanical Energy) / (mass x gravity)
Substituting the values:
h2 = (Total Mechanical Energy) / (103kg x 9.8m/s²)
By substituting the values into the equation and evaluating, you can find the height to which they swing up after the collision.