Answer:
I think Science,Math and Social
Tarzan (who has mass 80.0 kg) is running across the jungle floor with speed 7.00 m/s as
shown in Figure 1. Tarzan grabs a large bunch of bananas (15.0 kg) and grabs a vine in an attempt to swing up to his monkey who is 3.00 m above him as in Figure 2.
i. What is Tarzan’s momentum before he grabs the bananas? [2 points]
ii. What is Tarzan’s speed just after he grabs the bananas? [4 points]
iii. Can Tarzan swing high enough to reach his monkey? Justify your answer. [2 points]
We are given:
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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Momentum of Tarzan before swinging:
We know that:
Momentum = Mass*Velocity
Momentum = 80 * 7
Momentum = 560 kg m/s
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Speed of Tarzan after grabbing the bananas:
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
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Finding the Initial and Final KE and PE:Here, KE = Kinetic Energy and PE = Potential Energy
Initial and Final KE:
We know that KE = 1/2*(mv²)
Initial KE:
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
Final KE:
Final KE = 1/2*(mv²)
[where v is the velocity at the maximum point of the swing]
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
Initial and Final PE:
We know that:
PE = mgh
[where g is the acceleration due to gravity and h is the height]
Initial PE:
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
Final PE:
Let the maximum height of Tarzan be h m
Final PE = 95*10*h
Final PE = 950(h)
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Finding the maximum height Tarzan will reach:Here, KE = Kinetic Energy and PE = Potential Energy
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