tarzan has a mass of 100 kg and is 200m above the group and wants to slide down a nearby vine. the vine can only hold 400n without breaking. assuming he starts from rest and moves with a constant acceleration what is the longest time it can take for Tarzan to reach the ground?
tension= mg-ma
400N=100(9.8-a)
solve for a. Then,
200m=at solve for t.
To find the longest time it can take for Tarzan to reach the ground, we need to calculate the acceleration and use the equations of motion.
Step 1: Calculate the force acting on Tarzan
The force acting on Tarzan is his weight, which can be calculated using the formula:
Weight = mass * gravitational acceleration
Given that Tarzan has a mass of 100 kg and the gravitational acceleration is approximately 9.8 m/s², the weight is:
Weight = 100 kg * 9.8 m/s² = 980 N
Step 2: Determine the maximum tension the vine can hold
The vine can only hold a maximum tension of 400 N without breaking, so the maximum force acting on the vine is 400 N.
Step 3: Calculate the net force acting on Tarzan
The net force acting on Tarzan is the difference between his weight and the tension in the vine:
Net force = Weight - Tension
Substituting the values, we get:
Net force = 980 N - 400 N = 580 N
Step 4: Use Newton's second law of motion
Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net force = mass * acceleration
Rearranging the equation, we can solve for acceleration:
acceleration = Net force / mass
Substituting the values, we get:
acceleration = 580 N / 100 kg = 5.8 m/s²
Step 5: Use the equations of motion
To find the time it takes for Tarzan to reach the ground, we can use the equation:
distance = initial velocity * time + (1/2) * acceleration * time²
Since Tarzan starts from rest (initial velocity = 0), the equation simplifies to:
distance = (1/2) * acceleration * time²
Substituting the given values for distance (200 m) and acceleration (5.8 m/s²), we can solve for time:
200 m = (1/2) * 5.8 m/s² * time²
Simplifying the equation, we get:
400 = 5.8 * time²
Dividing both sides by 5.8, we have:
time² = 400 / 5.8
Taking the square root of both sides, we get:
time = √(400 / 5.8)
Calculating this, we find:
time ≈ 9.02 seconds
Therefore, the longest time it can take for Tarzan to reach the ground is approximately 9.02 seconds.