Question

Problem 8--Circular Motion and projectile motion: Tarzan (mass 80 kg) swings at the end of an 8.0-m long vine. When directly under the vines support, he releases the vine and files across a swamp. When he releases the vine, he is 5.0 m above the swamp and 10.0 m horizontally from the other side. Determine the force the vine exerts on him at the instant before he lets go (the vine is straight down when he lets go).

Answer 1

Answer:

1000 N

Explanation:

Let v be the his horizontal speed when he releases the vine and t be the time it takes for him to fly across the swamp and land.

Assume $g = 10 m/s^2$

When he releases the vine, there's only gravity acting on him downward. There's also no vertical velocity at this point.

Therefore, for him to travel 5 m vertically:

$s_v = \frac{gt^2}{2} = 5t^2 = 5 (m)\\t = 1 (s)$

Horizontally we have

$vt = s_h = 10\\v = \frac{10}{t} = 10 m/s$

For Tarzan to achieve this horizontal speed, the centripetal acceleration and force exerting on the vine at the instant before he let go must be

$a = \frac{v^2}{R} = \frac{10^2}{8} = 12.5 m/s^2$

$F = ma = 80 * 12.5 = 1000 (N)$