The conservation of momentum and energy allows to shorten the results for the movement of the girl on the trampoline holding the box are:
a) the girl's speed is v = 4.98 m / s
b) The speed of the girl + box system is: v_f = 0.996 m / s
c) the maximum height is: y = 2.05 m
Kinematics studies the movement of bodies, looking for relationships between the position, velocity and acceleration of bodies.
The momentum is defined by the product of mass and the velocity, when a system is isolated the momentum is conserved.
The mechanical energy is the sum of the kinetic energy plus the potential energies, when there is no friction in the system the mechanical energy is conserved.
Let's solve this exercise in parts:
a) Let's use kinematics to find the speed of the girl before she grabs the box
v² = v₀² - 2 g y₁
v² = 8² - 2 9.8 2.00
v = R 24.8 = 4.98 m / s
b) Let's use momentum conservation for when the speed of the girl and the box together. Let's write the moment in two moments.
Initial instant. Just before you grab the box.
p₀ = M v + 0
Final moment. Right after taking the box
[tex]p_f[/tex] = (m + M) [tex]v_f[/tex]
In system this form by the girl and the box therefore it is an isolated system and the momentum is conserved.
[tex]p_o = p_f[/tex]
mv = (m + M) [tex]v_f[/tex]
[tex]v_f = \frac{m}{m+M} \ v[/tex]
Let's calculate
[tex]v_f = \frac{15}{15+ 60} \ 4.98[/tex]
[tex]v_f[/tex] = 0.996 m / s
c) Now we use conservation of energy after the girl has the box.
Starting point. When the girl has the box
Em₀ = K + U
Em₀ = ½ (m + M) v² + (m + M) g y₁
Final point. At the highest point of the trajectory
[tex]Em_f[/tex] = U
[tex]Em_f[/tex] = (m + M) g y₁
As there is no friction, the energy is conserved.
[tex]Em_o = Em_f[/tex]
½ (m + M) v² + (m + M) g y₁ = (m + M) g y
y = [tex]\frac{v^2}{2g} + y_1[/tex]
Let's calculate
y = [tex]\frac{0.996^2}{2 \ 9.8} + 2.0[/tex]
y = 2.05 m
In conclusion using the conservation of momentum and energy we can shorten the results for the movement of the girl on the trampoline holding the box are:
a) the girl's speed is v = 4.98 m / s
b) The speed of the girl + box system is: v_f = 0.996 m / s
c) the maximum height is: y = 2.05 m
Learn more here: brainly.com/question/15095150
