tarzan(85 kg) tries to swing across a river hanging from a monkey rope(10m)long as he reaches bottom of his swing he os travrlling at 8m/s but he doesn't realise the rope has a breaking strength of 1000N.does he make it safely across the river

To determine whether Tarzan makes it safely across the river, we need to analyze the forces acting on him while swinging.

First, let's calculate Tarzan's weight, which is the force acting downward on him due to gravity:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given that his mass is 85 kg and the acceleration due to gravity is approximately 9.8 m/s^2:
W = 85 kg * 9.8 m/s^2 = 833 N

Now, let's determine the tension in the rope at the bottom of Tarzan's swing. At this point, Tarzan is experiencing two forces:
1. Tension in the rope (T) acting upward
2. Weight (W) acting downward

Since Tarzan is at the bottom of his swing and moving upwards with a velocity of 8 m/s, we know that tension in the rope should be equal to the sum of his weight and the centripetal force acting on him. This can be calculated using the formula for centripetal force:
Centripetal force (Fc) = (mass * velocity^2) / radius

Given that the radius of the swing is 10 m:
Fc = (85 kg * 8^2 m/s) / 10 m = 544 N

Therefore, the tension in the rope at the bottom of the swing is the sum of Tarzan's weight and the centripetal force:
T = W + Fc = 833 N + 544 N = 1377 N

Since the tension in the rope (1377 N) exceeds the breaking strength of the rope (1000 N), Tarzan does not make it safely across the river. The rope would break under the tension, and Tarzan would fall into the river.

To determine if Tarzan makes it safely across the river, we need to compare the tension in the rope to its breaking strength.

Step 1: Calculate the gravitational force acting on Tarzan:
The gravitational force can be calculated using the formula: F = m * g, where m is the mass and g is the acceleration due to gravity. In this case, Tarzan's mass is 85 kg.

F = 85 kg * 9.8 m/s^2 = 833 N

So, the gravitational force acting on Tarzan is 833 N.

Step 2: Calculate the tension in the rope at the bottom of the swing:
To calculate the tension, we need to consider both the weight of Tarzan and the centripetal force acting on him at the bottom of the swing.

The centripetal force can be calculated using the formula: F = (m * v^2) / r, where m is the mass, v is the velocity, and r is the radius of the swing. In this case, the radius is the length of the rope, which is 10 m.

F = (85 kg * (8 m/s)^2) / 10 m = 54.4 N

So, the net force acting on Tarzan at the bottom of the swing is 54.4 N.

Step 3: Compare the tension to the breaking strength of the rope:
The tension in the rope should not exceed the breaking strength of 1000 N for Tarzan to make it safely across the river.

Since the tension in the rope is 54.4 N, which is well below the breaking strength of 1000 N, Tarzan does make it safely across the river.