<u>We are given:</u>
Mass of Tarzan before swinging = 80 kg
Mass of Tarzan when swinging = 80 + 15 = 95 kg
Velocity of Tarzan = 7 m/s
The height of the rock Tarzan's monkey is sitting on = 3 m
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<u>Momentum of Tarzan before swinging:</u>
We know that:
Momentum = Mass*Velocity
Momentum = 80 * 7
Momentum = 560 kg m/s
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<u>Speed of Tarzan after grabbing the bananas:</u>
The momentum of Tarzan will remain the same but his mass will increase
So, Since Momentum = New Mass* velocity
560 = 95 * v [where v is the velocity of Tarzan]
v = 5.9 m/s
<u>__________________________________________________________</u>
<h3><u>
Finding the Initial and Final KE and PE:</u></h3>
<em>Here, KE = Kinetic Energy and PE = Potential Energy</em>
<u>Initial and Final KE:</u>
We know that KE = 1/2*(mv²)
<u>Initial KE:</u>
Initial KE = 1/2*(mv²) [where v is the velocity after picking the bananas]
Initial KE = 1/2*(95*5.9²)
Initial KE = 1653.5 Joules
<u>Final KE:</u>
Final KE = 1/2*(mv²)
<em>[where v is the velocity at the maximum point of the swing]</em>
Since Tarzan will be at rest at the maximum point of the swing, v = 0 m/s
Final KE = 1/2*(95*0²)
Final KE = 0 Joules
<u>Initial and Final PE:</u>
We know that:
PE = mgh
<em>[where g is the acceleration due to gravity and h is the height]</em>
<u>Initial PE:</u>
Since the height of Tarzan from the ground was 0 m at the beginning of the swing, h = 0
Initial PE = 95*10*0
Initial PE = 0 Joules
<u>Final PE:</u>
Let the maximum height of Tarzan be h m
Final PE = 95*10*h
Final PE = 950(h)
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<h3><u>
Finding the maximum height Tarzan will reach:</u></h3>
<em>Here, KE = Kinetic Energy and PE = Potential Energy</em>
From the law of conservation of momentum, we know that:
Initial KE + Initial PE = Final KE + Final PE
Replacing the variables:
1653.5 + 0 = 0 + 950h
1653.5 = 950h
h = 1653.5/950 [dividing both sides by 950]
h = 1.74 m
Therefore, the maximum height reached by Tarzan is 1.74 m
but since his monkey is sitting 3 m high, he will NOT be able to reach his monkey
